No game mechanics are mentioned in the story, so why wouldn't there be a portal gun? Extrapolating, if one is in a time travelling ship, the portal gun could actually generate portals between different time dimensions, and I can already think of a ton of gameplay ideas that could use this concept.
Using the portal gun to not only jump through space, but time as well?
Ummm, YES!
The 'structure' of the puzzles you could use that with would need to be very tightly controlled (enemy position vectors, amount you can travel backwards in time, maybe some sort of energy mechanic you have to pick up as you go along, etc). But still, WOW! Jumping back to the start of a level at the very end and you must manipulate time to accomplish the level, there is a LOT of possibility to talk about there. I have no idea what jumping forward in time would look like except if you went back, say 5 minutes, and then you could only go forward again up to that 5 min mark.
However, you can't use this in a PvP manner very well, only co-op. Maybe you could have the players ALL jump back in time except the user of the time device who got to essentially teleport around. However, the cheesing of that mechanic would be frustrating in the extreme.
