The biggest problem of selling a game piecefold is that the first part is nothing but ads for the second part.
Depends. Competently executed, a first episode can be perfectly self-contained while still whetting the appetite.
I haven't really played any serialized games other than Walking Dead, so I don't have a good example off the top of my head, but film's rife with them. Star Wars and The Matrix are both excellent first acts that end with satisfying closure while still leaving the major arc unresolved. (Indeed, both of those first chapters have far better and more satisfying resolutions than their complete arcs.) Course, those are also cases where the parties involved didn't know if they'd have the money for a sequel and figured they HAD to be self-contained -- does that make Lord of the Rings a better analog? Probably not, given that it was based on a beloved novel already conveniently split up into three parts, and was the equivalent of a big-budget AAA title rather than the more modest fare we see in episodic games.
I haven't gotten around to playing 400 Days but I'm guessing it's probably a pretty good example of a self-contained story that's part of a larger narrative. It's a bookend between two arcs, though, not a first episode as such.