How to remove stripped logic board screw?

If you have some of the head left then you can try and apply more pressure and turn the driver slowly.

If it is completely striped, then your options are pliers or drill.

If you can get needle nose pliers on the head and have enough grip to turn it, turn slowly, and be careful not to scrape the board.

You can also use a drill with a drill bit as close to the same size of the screw as possible and apply some, not a lot of pressure, straight down and use the lowest speed to slowly drill the head away, once the head is off you can remove the rest of the board and use pliers to remove the remaining screw.