I don't know of any technical reason why they should scan horizontally — except that the screen is wider than it is tall, but early TVs were fairly square. Maybe they scan horizontally because oscilloscopes did, because we plotted graphs horizontally, because we read horizontally? Maybe there's a parallel world (or in this sense a perpendicular world) where we read top-to-bottom and TVs scan vertically first and horizontally second? Honestly I think if the first TVs had worked that way, it would never have been considered enough of a problem to be worth the work to fix it. After all, TV would have been completely unaffected.

Early videogames, though? They'd have been radically different. Some tragic losses, and some interesting opportunities. I don't know what games would have looked like, and many of them would be exactly the same, but a lot of things would be radically different.

Palette swaps

The water at the bottom of some Sonic levels uses a palette swap to apply a blue tint to everything in the water. The bottom UI in Lemmings 2 (at least on Atari) uses a different palette to the game. There's a racing game that uses a chunk of VRAM as extra memory by storing data in the sky and hiding it by switching to a palette that's all sky-blue while that area's being drawn. You couldn't do this if the screen scanned vertically — you could only change the palette in vertical stripes. So expect lots of waterfalls and tall shadows in platforming games, and more vertical UIs docked to the sides of the screen. That'd probably work better anyway, if we're assuming text is top-to-bottom too.

An advantage for a game like Sonic is, when you do a dash of any kind they could move the Sonic sprite across the screen as the image is drawn to give a "smear" effect to show him travelling at ridiculous speed. Not sure if that'd interfere with gameplay but it'd look great.

Parallax scrolling

Lots of games used horizontal scanning to create 3D looking backgrounds — they'd have a background with clouds, then mountains, then nearby land, then water, or whatever, all arranged in neat horizontal stripes, and then move the background left and right while the image was being drawn so that it looked like different parts of the image were scrolling at different speeds, which looks like layers. You can't do this effect on a vertical-scrolling level — so in vertical-scanning world, expect to see a lot more vertically scrolling levels. I'm thinking the sci-fi action blaster games where you'd be climbing a skyscraper of some kind.

There are a handful of horizontal pipe-style levels too — any shape can be made as long as it varies only vertically. Obviously, this becomes horizontally in the new world so vertical pipes and towers are the new sewer levels.

I think this is also used for heat-haze sometimes, but that's out now. Instead, expect a lot of dynamically rippling water — we can draw a sprite for the surface of water, and move each vertical row of pixels up and down independently, even if normally the system draws everything in 8×8 sprites.

Mode 7

MarioKart works because the Super Nintendo is very good at drawing one background layer in a perspective view. But actually the SNES can't really do that — all it can do is rotate and scale that layer. The perspective effect is created by scaling the layer more and more the further down the screen you get. Bigger looks like nearer.

So the real-world SNES can't show a vertical plane, only a horizontal one — but the vertical-scanning SNES can only show vertical ones. So while MarioKart couldn't exist, Wolfenstein-like faux 3D could be lightning fast, and I expect there'd even be a 3D webslinging Spiderman game on SNES where you flew down a narrow street collecting things, shooting webs at other things, avoiding yet further things, all while using L and R to grapple onto buildings to keep yourself from crashing into the walls or hitting enemies.

There'd likely also be a MarioKart-like game but played vertically. Christ only knows what the presentation would be on that — there really aren't any real-world vehicles that move that way. I can see F-Zero working for this — the races happen within giant "screens" that everyone can watch for miles around. You can knock the other players into the sides of the screen rather than (as well as?) off the track so there's more 3D to it — but if future games on really 3D systems kept this unusual angle, you wouldn't be able to jump because there are no directions left to jump in.

I expect there'd also be a Mode 7 kart racer eventually, probably released by CodeMasters because those guys just don't give a shit, which required you to put your TV on its side to play. Great for arcade bars that could just keep it set up for a cheap game machine, I guess.

Sprites in a row

Mostly your classic Mario-style games wouldn't be affected really, though — but one limitation that comes up from time to time in old games is that you can't have more than a certain number of enemies on the same horizontal row. Really you can't have that many enemies on the screen at all, but if they're at different heights you can swap them in and out as the screen scans. In our world, that means they can't be at the same height, but in vertical-scanning world, it means they can't be at the same horizontal position. This would likely be much less limiting for platformers and the like, and would probably affect the shapes of attack waves in all those vertical-scrolling arcade spaceship shooter games that would be coming out for the system where vertical effects are easy.