Those two boards control the #86 lights on the metal ramps. notice when you turn the game on, before the CPU has even "booted", that the left side ramp lights are moving. This board controls that.
Then there's a relay under the playfield, that when engaged, turns off the left side ramp lights, and turns on the right side ramp lights (which the other identical board controls). but the CPU is not involved in making these lights go in sequence. These boards just require 5 volts and does that the sequencing itself. This is a standard board, used on a lot of sys80 games for light effects, without using any CPU board processing. The only thing that changes are a resistor or two to change sequence timing.
The reason the board is burned is that the ramp lights can short against the metal ramp. It's pretty easy to do. If this happens it can causes a dead short and smoke that lamp board.