Its not the pins that you need to bend slightly, its the gates/shiutters that the pins make contact with on the PSU board. I have had several Dreamcasts, all that eventually show this problem. Take the PSU board out and look at the gates/shutters that the pins push though to make contact with. Looking down on top ofthem, push them down with a terminal screw driver so that they push harder against the pins when put back in place.
The reason you will only get this issue when playing a game is because the dreamcast will be trying to draw a larger current from the PSU.
Its is also worth cleaning the pins with a contact cleaner or glass fiber brush if you have any. Its not essential though. Im an elevtrical engineer so have this sort of stuff.
Hopefully this will help you.
Dreamcast: Blue Swirl, 60hz, White LED, Removable battery holder, Internal SD card reader, BBA, DreamPi, RGB Scart