It is possible that your download procedure has not preserved the executable flag on the file. Open a terminal and navigate to the folder where the bin file is saved, and type "chmod u+x atk*.bin", and then run it using "./atk-12.1.1-linux64.bin".
There is, however, no difference in terms of core utilization between Windows and Linux, that is an incorrect statement. Running ATK on Linux can however be faster because there is typically less OS overhead; of course, if Windows uses one core more or less constantly, that core is not available to ATK.
ATK supports all graphics card, but the important point is what driver you have. You should make sure to use the NVidia vendor driver, not the one which comes with your Linux distribution.
