Sergey, you are expecting to much from the Intel HD 4000 graphics. It is not a powerful gaming chip. You are using a resolution that is straining the HD 4000 to much. You saw that yourself with the 3D Mark test at 1920 x 1080, or lower.
LinX, Aida, and Memtest do not test the graphics chip/core, so while you have shown your CPU and memory is working fine, your testing of the HD 4000 at 1920 x 1080 clearly shows that is the weakest part of your PC.
This is a chart comparing the performance of common graphics cards and chips, the HD 4000 is in the list, near the bottom:
PassMark Videocard Benchmarks - Common Videocards
Your CPU and memory is not the problem, during gaming, they are not being used very much compared to the video chip or video card.
You don't have a 'K' version of the i7-3770 CPU, so you don't have any way to over clock the video processor, correct?
Your system report you posted in the Intel forum shows you have the latest driver released by Intel, so nothing to do about drivers.
All you can do is reduce the resolution when gaming, or get a separate graphics card with better performance.