Вместо того чтобы идти в школу, он остался дома, играя в видеоигры.
It's a mistake. The participle (играя) is using wrong here. How iCake said "Играя implies a continues action simultaneous with the main verb, which is остался. This is where the problem lies, остался is a completed action, but играя is not."​ Your variant is correct.