I'm looking at them now and I don't see why you couldn't port games like that to TIC-80 within the restrictions . I would recommend looking into Moonscript so that the transition is a bit smoother from Haxe since it has a similar object-oriented syntax. It wouldn't be a completely simple port, but if you get a handle on the TIC-80 functionality it would not be terribly difficult.
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I bought a copy about an hour before I originally posted. I'm sure that Unity is the reason. I'm fairly certain that Unity requires a version of OpenGL not available for my card. I'll just have to wait until I build my desktop to use it, but this looks like a really awesome tool and I can't wait to give it a spin!