But he did die! Twice! Once in the light orange cave right before the bridge and once in the second underwater area!
Good thing dying is quick and causes funny warps.
While I was unable to fully replicate the glitch on console, I have been able to test each component and it IS possible in theory on console. Additionally, having debugged this glitch and seeing the ASM involved, there is no reason why this would be from inaccurate emulation. If you actually read the technical document that Masterjun included, you would know this glitch works by changing the game mode (RAM address $0100) by manipulating the stack, RNG, and OAM mirrors. I can confirm with an extremely high degree of certainty this is not an emulator specific glitch.
Even if this isn't an emulation glitch, what are the chances it would happen on an actual console if you provided the same input? It seems like runs that heavily abuse the RNG and the contents of RAM would be impossible to replicate when you can't see the RAM...
You could also try Metroid 1 + Metroid 2 for a cross-platform TAS. The NES and Gameboy share control schemes so it's not like there's room for ambiguity. I think that'd work better than trying for more recent titles.
Metroid would be a LOT more difficult. Games like the MegaMan series and the SMB series involve mostly moving to the right with some jumping, so a lot of the work appears to be making sure all of the jumps either happen at the same time, or happen while the other game isn't accepting input (like between levels, going down a pipe, etc). The early Castlevania games would probably be workable this way too, although I'm not brave enough to try it :)
With the Metroid series, you would also have to make sure you were the player in each game was moving the same way at the same time. So if you needed to go four screens left in Metroid 1 and 7 screens left in Metroid 2 at a given point, you'd somehow have to delay Metroid 1 by the time it took to go the extra three screens in Metroid 2. Which I suppose is possible, but it would slow down the run drastically.
That said, this Mario movie is the best multi-game run I've seen yet! I was pretty blown away by the MegaMan 3-4-5-6 run, but that isn't so shocking because those are all pretty much the same game...these are different games with some character overlap!