Alienware X51 R2 vs Alienware Alpha

My new system:  Alienware X51R; i7-4770; 16 GB Dual Channel DDR3 at 1600 Mhz; 2 TB 7200 SATA 6Gbs; 2 GB GDDR5 NVIDIA GeForce GTX 670; Windows 7  64-bit.  You have accidentally stumbled on a very pertinent issue for me by writing up your system as a Windows-7 based XBMC desktop "connected via HDMI to a...1080p/HD-7.1 Home Theater System."  I currently have the Alienware described above & am quite happy with it.  However, my second, older "back-up" computer needs to be completely replaced, and I've been trying to select a product which will serve as BOTH a desktop computer AND a media link to my 4 year-old Samsung semi-smart 1080p HDTV.  As background, I have used PS3 for the past 4 years as a Blu-Ray Player and, courtesy of the PS Network, I have added Netflix & YouTube to my TV (& play the occasional PS3 game as time allows.)  Unfortunately, PS's browser is terrible - hence my desire to find a computer that will allow me to freely roam the Internet with any browser I desire as well as allow me to access XBMC.  My knowledge of the latter is almost zero, but I understand it is critical to use it in order to "freely roam." 

So, when I first read about Alienware Alpha 3 days ago, I thought I had died and gone to heaven.  But I'm wondering now if you can confirm that I really have? Do you know whether Alpha will achieve everything I want it to, i.e., allow me to use MS Word; use it for email; and any other common desktop function under Windows 8.1, on both a monitor and/or my HDTV?  Playing games on Steam is a good feature, especially if my HDTV will allow Alpha to link to it, but it is not as relevant to me as a browser which will let me access XBMC and everything that will bring to my HDTV. Or would I be better off simply buying a less expensive computer than my X51, but with enuf power and a decent graphics card to both use as a "desktop" and also hook up via HDMI to my HDTV as you have?  Because you have XBMC on your system, I thought you just might be able to do me a huge favor by providing me with your opinion on this - although I understand that you have not used Alpha as such (and it does not matter to me that you do not have an X51).  Finally, when you state that your entire system is "fully Windows gaming capable," do you mean by buying Windows PC gaming software and downloading it to your system so that you can play it on your HDTV?   Many thanks!