Ok after couple of tests I can confirm, the issue seems to be fixed now. Ingame overlay and achievements are working fine.

Note those who had that issue:

1. You need launch both RTST and PS2 under Admin mode (if you use steam version of the game, then do not launch it using steam, but just use Admin mode on "LaunchPad.exe").
2. If overlay still does not come up, then make sure that you change under options Auto to x64
2. Your game must be in full screen.

Also I noticed when I closed my game down RTST gave me that D3D com. Error. on top of the RTST, seems to be just visual message, nothing what could affect RTST usage.

Thank you so much, for fixing the problem so fast.