I would not think the LED intensity will effect the heat on the DLP chip. One end of the light engine is the LED light source, shining well timed pulses of R G and B light at the DLP chip, where a few million micromirors toggle between two positions ~5000 times a second to either reflect all or none of the R,G, or B light to a specific pixel. If the pixel is solid white or solid black the mirror for that pixel could be immobile and that pixel would not be generating any load/heat. Each of the ~2 million pixel/mirror elements are independent. If the pixel is to be 50% illuminated grey, the mirrors are toggling on and off the most to make the pixel ultimately look grey. At least that is my understanding.
Playing games or watching one program over another should not make a difference in how hard the chip works. Unless you watch nothing but 100% white or black screens a lot. The DLP chips fail over time. Heat sinks get dirty and dusty. Heat damage is cumulative, and then one day you get your first dot. Maybe the duty cycle of the set went up, if say, you normally watched TV like an hour or two a day, and then the grandson comes over and plays games for 10 hours straight, maybe that could make a difference.