New laptop recommendation?

You're not going to find a Latitude system that's built for gaming.

That domain is the Alienware and at the low end, the G-series Inspirons.

You'll then need to prioritize, since one system won't meet all your specifications.  

If you want true, discrete, hardware-controllable GPU, that leaves the G-series behind.  You now have the Alienware 15 or 17 models to choose from.  If you're going to be gaming for hours, the 17 chassis is better suited, but less portable.  If portability (slim and lighter weight) is important, you sacrifice gaming for it;  conversely if gaming is the goal, forget slim and light.

Your call - but the Alienware 15 is the best compromise.

@Mustey  Sorry for the triple post here, but one other thing to be aware of when shopping for 15.6" laptops is the question of whether the keyboard will include a number pad on the right.  Some people want that because they rely heavily on it (such as my dad, who owns an accounting firm), while others don't want it because it causes their hands to be left-shifted on the palmrest, which can make resting your hands on a laptop more difficult.  It can also complicate typing while you're balancing your laptop on your actual lap, because your weight and the force of your typing is offset to the left rather than centered.  The Latitude 5510 and 5511 both have number pads.  The XPS 15, Latitude 9510, and ThinkPad X1 Extreme systems do not.  All of those systems are also thinner and lighter than the Latitude 551x systems I mentioned -- but the Latitude 9510 and XPS 15 don't have touchpad buttons at all, and the X1 Extreme systems only have buttons between the touchpad and keyboard.

Also, I don't know how much of a keyboard power user you are, but you might want to take a close look at the keyboard layout of each system.  In particular, Dell has taken some flak recently for relocating their Home/End keys.  On older systems, those keys were activated by pressing Fn+Left/Right, which was convenient because PgUp/Dn were activated either by pressing Fn+Up/Down or by dedicated PgUp/Dn keys around the arrow keys on certain models.  Either way, it means that those four keys were all in the same area, which was handy because they're often used in quick succession for navigating interfaces and documents.  But now on some laptops, including ALL of the Dell systems I've been talking about, Home/End are placed on the top row, quite far away from PgUp/PgDn.  That change has generated a ton of complaints from users in various threads here from people who have come from older Dell systems.  By comparison, the X1 Extreme has those keys in the top row as well, although it's better in two ways.  First, it has dedicated Home/End keys there, so you don't need to press Fn to activate those keys as you do with the newer Dell systems.  And second, Home/End can also be activated by pressing Fn+Left/Right, even though those keys aren't labeled as such, which works nicely in conjunction with the dedicated PgUp/PgDn keys directly above the Left/Right keys.

@Mustey  Latitude 5510 and 5511 are probably your only options if you really want all of those things you listed.  And you might need to specifically order the "dual pointing" option to get the touchpad buttons you want, but I'm not 100% sure about that.  But I'll share a few additional thoughts:

• The touchpad with external mouse buttons is going to knock out a TON of options these days, unless maybe you'd consider "dual pointing" laptops as satisfying that requirement.  Those would be laptops that have both a touchpad and a "pointing stick" (erase-style nub in the keyboard), and therefore will have dedicated clickable buttons between the touchpad and the keyboard.  If you could make yourself use the pointing stick or get in the habit of clicking buttons that were above the touchpad rather than below it, then you'd have options.  Otherwise, that requirement especially in conjunction with wanting a thin and light system is going to be a major limiting factor, because nowadays even the larger systems like the Precision 7000 Series that used to have dedicated buttons (for a while they even had a dedicated middle click button!) have dropped them in more recent generations.  The two Latitude systems I mentioned above have two sets of clickable buttons though, one for each pointing device.
• Be aware that there are two very different iterations of the Core 10th Gen CPUs out right now.  There's the "Comet Lake" architecture that's just yet another minor refresh of an architecture introduced with Broadwell (which was Core 5th Gen), and then there's "Ice Lake", which is a completely new architecture using that includes a 10nm manufacturing rather than 14nm and includes a much improved GPU.  But Ice Lake is only found on relatively low powered systems like the XPS 13 at the moment.  Few if any 15.6" systems will have those CPUs; they'll instead have Comet Lake.  I mention this mostly because if you'd end up with Comet Lake at best anyway, you shouldn't necessary rule out 9th Gen CPUs, because the difference between 9th Gen and 10th Gen Comet Lake is minimal.  (Yes, with Core 10th Gen, Intel found a way to make their CPU naming even more confusing than it already was, which is really saying something!)

The downside to the Latitude 5000 Series systems I recommended is that they're not especially thin and light relative to other models.  But those other models I'm thinking of don't have dedicated touchpad buttons.  If you were willing to give up on the touchpad issue, then that would open up the Latitude 9510 and XPS 15, the latter of which would only be true when ordered without an NVIDIA GPU.  Both of those would be thinner and lighter.

The ThinkPad X1 Extreme Gen 3, the would also be well worth considering, if you're not necessarily committed to Dell.  I have the Gen 2, which is quite similar, and I love it.  But the Gen 2 can only be ordered with an NVIDIA GPU.  The Gen 3 is available in an Intel-only configuration.  I posted some thoughts on the XPS 15 9500 vs. the X1 Extreme here if you're curious.  If you use a lot of keyboard shortcuts and you'd be new to Lenovo, just make sure to enable the BIOS option to swap the Ctrl and Fn keys, since the ThinkPad systems have those keys backwards relative to the rest of the industry -- which is why it's so great that Lenovo offers that BIOS option, otherwise the muscle memory of anyone coming to them from another brand would be completely destroyed.

@ejn63  The OP said he wanted NO discrete graphics, which I take to mean a system that only has an Intel GPU.  And he said NOT for gaming.

@Mustey  I forgot to add that if you're curious what the difference is between the Latitude 5510 and 5511, it seems to be:

• The 5510 uses Intel's low power "U Series" CPUs, which will be better for battery life.  The latter uses their higher performance "H Series" CPUs.  But both are based on Comet Lake, not Ice Lake.
• The 5511 has Thunderbolt 3 and HDMI 2.0.  The 5510 only has USB-C with DisplayPort Alt Mode and HDMI 1.4.  Thunderbolt 3 allows you to use Thunderbolt peripherals, and if you think you might want a docking station, having Thunderbolt 3 on the 5511 will mean a Thunderbolt dock would be able to tap into 4x more display bandwidth than a USB-C dock paired with the 5510.  So whereas a regular USB-C dock when used with a Latitude 5510 would be limited to dual displays up to 1920x1200 each or a single display up to 2560x1600, a Thunderbolt 3 dock paired with the 5511 would be able to run dual displays up to 4K 60 Hz each or triple displays up to 1440p each.  And HDMI 2.0 available on the 5511 supports up to 4K 60 Hz displays, whereas HDMI 1.4 on the 5510 only supports 4K 30 Hz or 1440p 60 Hz.