Golden Axe for DOS does seem to have CGA, EGA, Tandy mode, and Hercules modes as well. I can;t find any video on the EGA version, but here is what the CGA version looks like:
https://www.youtube.com/watch?v=uoimkm9Uq8c
The scrolling doesn't look too bad all things considering.
Yeah I saw that but couldn't find a video quickly when I looked. It's light years better than most CGA games I've seen, but it's still jerky (especially at about 2:33). However, this is likely ran from an emulator with god knows what specs and changes. My point in pointing out the VGA thing is that it's a different set of hardware, and VGA made it much easier to do (and also that i'm not 100% sure I buy the authors explanation of what he's doing there as there were other ways of doing that for VGA than modeX.)
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One of the problems to understand this in context is not when the game was released and what was around it, but rather, when each of these things were being developed and what information they had access to. If we consider simply the release of examples, much of this may have been done first in the demo scene.
Few people had access to the internet in 89 and 90, aside from maybe some usenet access. This made it much more difficult to share neat tricks. Usenet, Dr Dobbs, and books like Michael Abrash's books were common. It's difficult to know what was around while they were developing and what Carmack had access to. This was especially true at the time for shareware developers like id. Undoubtedly, the development timelines for all of these were overlapped, and the engine was likely partially in development the year before. (Though the line between tinkering, learning, and full engine development may have been thin). So regardless of which hit the market first, it's at least possible that Carmack had never seen them before he had finished the basic technique. It's also possible, if not probable, that he didn't have the same access to information as some of the larger companies doing ports.
As an additional thing, Golden Axe, at least according to MobyGames was done by Team Shinobi, who had also worked on other dos ports, and their earlier work was just as unsmooth.
Altered Beast and maybe shadow dancer (can't find verifiable videos that aren't emulators).
As for the demo scene, their development cycles could be much shorter as they were basically tech and skill demos, and not full-fledged games. They had a ton of techniques that were impressive to do things like emulate true color with VGA and some cool 3d techniques. There were at least a few games that came out of some of those demos.
FWIW, I don't know the exact state or what Carmack had access to, and I haven't read the book. It's clear that the industry was converging on smooth scrolling, even without Carmack, and it would have gotten there at the same time it did. It's entirely possible that id was playing catch-up and just came up with a catchy name and a "difficult problem" for sake of marketing. Keen was released earlier enough and was shareware so largely accessible, so it makes for a great story, and may still have been one of the first smooth-scrolling games most pc gamers had seen.