Second problem, much less frequently noticed. Your finger is in the way. It's often very important to get a very precise position in those games, AND you often need to see when the pointer changes colors, patterns, etc, indicates you're over the thing you can click on etc etc. On a touch interface, your finger is covering the pointer. It doesn't need you to see the pointer because you can't hover anyway. So if you fix hover, you have this new problem.
Very perceptive! (do you have an iPad?) Anyway, you are correct... and that aspect has not been discussed much. Even for insertion point positioning and text selection (such as I just did while editing this post), Apple pops up a little magnifying glass which shows me (from its offset location) the area under my finger. So yes, I would certainly think that any game (or website gateway even) in which any degree of precision when pointing is needed, would also require retooling.
Excellent... I'll keep this in mind now, as I do battle in forum threads.
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Here are two old articles which provide some perspective (on the Flash topic in general, not the touchscreen issue):
