Sorry to hear that there were lag issues with the web build :( If you're interested, I can send you a steam playtest key so you can run it that way, which hopefully wouldn't have those issues. While the introduction to the game is certainly a bit more puzzle-platformer-esqe, this is primarily to teach some important mechanics in the game, and it opens up more into an arcade-y strategy game after the introduction. All this said, I'm currently finishing up a new build (that has been a work in progress over the past month, roughly) which makes many changes, including the intro section of the game.
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This is one of the major changes I've already made to the introduction in the new version (which hasn't been released yet). I agree that in the version you played, the point at which it is introduced is just not great, and can easily set the wrong impression for what the game is going to be about lol