It’s Another Simulation
After you got kidnapped by the Zin, Saints Row 4 took place primarily in a simulation version of Steelport. Zinyak had the ability to change and warp the simulation to any way that he saw fit, but he mostly did this in small, subtle ways, like sending in powerful Wardens after you if you got too unruly or by just adding statues of himself and billboards telling you to obey his rules and accept your fate. Primarily, he found your simulation the most amusing one out of all the captives he had.
The simulation was a lot of fun, but Steelport can also understandably lose its luster. It could be somewhat possible that the President is just going through another simulation of their own design to stave off the boredom of traveling space. You can only have dance parties for so long, after all. This being another simulation would also be able to explain how the L.E.G.I.O.N. villain Dr. Babylon is able to call down monsters from space, which also happens to look suspiciously like the Wardens from Saints Row 4. This would also justify the red and black motif that L.E.G.I.O.N. seems to have (also borrowed from the Zin), along with the designs of the enemies seen in the trailer. Plus, there’s a bunch of technical hiccups in the video showing off the Agents that could hint at this being a game within a game as well.