X-Space '92 Mini-Game:
In the Madness Level, before you get to the 3rd checkpoint, enter the room with a guard at its door. Use Telekinesis to get the disk upon the shelf and put it into any computer in the level.

Earth Impact Mini-Game:
In the Reliance Level, there is an arcade machine in one of the rooms in the Main Building.

Thanks to Revolution readers Arcana and Immonen!