A F-15 could land on a carrier and the LDG could take the stress. The tail hook could also take the stress as I am sure many F-15 have made hot landings and engaged the barrier cable. The F-15 has the power to make a take off from a carrier but not a cat launch as it has no attachment on its gear for a hookup. A Cat launch would rip the nose gear off of a F-15. Clear the deck, give it enough room to get up to speed and it could get off of a carrier.
theres a lot of plot holes in the story...the F-15s most likely were spoused to be something else. or they just got lazy with the story.
I don't think you understand the structural difference between land-based and carrier-based aircraft.
There was an idea to make a naval version of the F-15--one with gear which could take a hard landing and one whose tailhook could support arrestor gear.
But it was canceled because it was a stupid idea.
If you landed an F-15 on a carrier you would break its undercarriage and its tailhook would rip off--look at the Israeli example when they tried landing one on the ground at similar speeds to what you would land on a carrier at..