A source (PC, PS4, Xbox) HDMI out port cannot upconvert to a monitor DP or mDP in port via a straight cable.

What you bought is most likely designed to do the opposite =
Source DP out port --> DP to HDMI adapter --> Monitor HDMI in port

You would have to purchase an HDMI in to DP out active converter. The PS4 HDMI out can only work in the following ways with the U2412M =

PS4 HDMI out --> HDMI to HDMI cable --> HDMI in to DP out converter --> DP to DP cable --> U2412M DP in port

PS4 HDMI out --> HDMI to DVI cable --> U2412M DVI in port

PS4 HDMI out --> HDMI to VGA converter --> VGA to VGA cable --> U2412M VGA in port

https://www.amazon.de/CSL-Adapter-Stecker-HDMI-Buchse-Beamer/dp/B003MPM4L8

This Works too?

That is a 1080/Full HD Source HDMI out to Monitor DVI in converter. In theory, it should work. But you would need two cables.

Source HDMI out port --> HDMI to HDMI cable --> HDMI to DVI converter --> DVI to DVI cable --> Monitor DVI in port