1) Noise cancelling headphones.
2) If the above doesn't work, then move.
Most games use the NDK and contain binary compiled specifically for ARM. Obviously those apps will not run on the MIPS processor.
Um... Unless they are recompiled to run on MIPS? I don't really see the problem as GCC already supports this.
Did anyone even read TFA?
Assuming that laptop does in fact have tracking software that can report on the applications that are running and/or be used to send screenshots back to your employer, your ideas to run standalone apps from a USB drive would only land you in "trouble" because the screenshots would still show "rogue activity". The other idea of imaging the whole HDD, re-installing, and imaging back sounds like more hassle than it's worth. But at least from this I know that your BIOS isn't locked down to the extent that you can't boot from external media. So...
What I would suggest is to run a standalone OS from a USB thumb drive or CD / DVD. In doing this, you can run the alternate OS of your choosing, while sidestepping the considerable hassle of creating the backup image, installing the other OS... Here is a rather comprehensive list from which you can choose. Knoppix, Ubuntu, or Mint are the ones I would try first.
"Ninety percent of baseball is half mental." -- Yogi Berra