Despite their complete lack of attention while reading, if indeed they do read the received requests, I somehow managed to get my problem signaled. Even though I told them that I ran a stress-test for my GPU, and that the temperature did not reach dangerous levels, they asked me to do it again. After that, they asked for a dxdiag, some networkinfo log, and a network connection test or something which is done by a site. The next step was advising me to add the game to the firewall's list of exceptions, which has already been done automatically, but who knows (even though that doesn't seem not even closely related to my screen shutting itself down).
The fact that they do not read the request and just answer using an already specified pattern (something like: Look, if this individual presents these problems, you replace the name with his, and just copy-paste this text, hoping him to think that you really care about solving his problem.) was, in my opinion, making me waste some time, due to the fact that they made me run again the tests which I already did, giving them the same detailed answers that were already specified in the initial request.
I was even told to check some page in which gameplay issues, like running in low FPS or having trouble connecting to the game were treated, like an additional advice, but again not even close to the cause of my real problem, or that their game uses about 1.5 GB of RAM. (This thing was pretty suspicious, due to the fact that it is not really some great graphics game or, I don't know, a one which should have the right to ask for this much.)
Now I am waiting for their next advice; sorry for the long story thing, thank you for your earlier concerns and I will let you know whether my problem is solved or not.