Further edit: I have no idea why, but in my head the color palette shifts when the screen is reversed, like all the colors get 20% darker. (Perhaps I'm analogizing with A Link to the Past's "Dark World", which isn't really the same thing, but you are welcome to explain that to my subconscious at your leisure.) It doesn't seem like there's a good reason for that from a Portal point of view, but it would offer a subtle hint that you're supposed to be going the other way now.
The idea that Stabyourself puts forth is arguably the default answer, in the sense that it is the usual one, but while basically functional, it never ever feels right. I just got done with Catherine recently which does the same basic thing (albeit with going behind something instead of going through a portal, but it's the same reversal problem) and 18 hours into the game it still felt unnatural... and that's hardly the first time I've encountered the "keep going a certain direction while held, then completely rekajigger the interface at an arbitrary point in the future when the user recenters the controls", either, so it's felt unnatural for even longer than that. (For bonus points, play on an Atari 2600 controller that just likes to cut out for a frame or two every so often, so the effect is that the game's controls appear to simply spontaneously revert.) Flipping the world would at least be changing things up.
Like the afore linked Super Mario Crossover, I see this and wonder, "how did they NOT make this?"
But as of now, most of the enemies in Mario were designed to be adequate hazards for a character who can only walk and jump, the matchup becomes pathetic if he's suddenly equipped with a Portal gun. From the video it seems the game-makers will have to be more creative with how Mario can be killed (Great heights, ranged attacks, time-trials, as opposed to just touching a mushroom/turtle/pipe plant)
No but seriously, this is super cool.