You're really asking two questions: why was your question closed as problem-not-puzzle, and why was the other question not closed? These are largely independent questions, and in general I would recommend that if one of your questions is closed you should focus on that rather than looking for other questions that should have been closed if yours was. Sometimes questions don't get closed that should be, so the fact that some other question survived isn't evidence that yours should have.
Your clock question
I think this question would have been closed even if you'd said it was from a puzzle quiz. It doesn't matter where it's from, it matters what sort of question it is.
The main criterion we use is: does solving this require some sort of insight or clever idea, rather than just following a standard procedure? Your puzzle about the clock is basically a matter of arithmetic.
See e.g. Proposed policy on mathematical questions, which is the nearest thing we have to an official policy; and Are math-textbook-style problems on topic? and its top-voted answer, which offers a bit more explanation of the puzzle/problem distinction.
 Well, sometimes it does, because e.g. we don't accept questions that come from currently-active competitions. But that doesn't change whether something's viewed as a puzzle.
The hexagon question
It's a question that's easy to pose and not so easy to answer. There's at least one solution that involves a clever idea (using the relationship between area, perimeter and inradius).
The fact that it involves some mathematical technicalities isn't an objection to it. See e.g. the second Meta question linked above, or What tricky mathematical questions are on topic here? which specifically addresses the question of whether involving mathematical technicalities is a problem. (The votes on the various answers indicate that the community doesn't think it is.)
Having said all that, this question can also be solved pretty routinely if one is so minded (e.g., one can write down the coordinates of all the vertices of a hexagon, and then there's an ugly formula for the inradius of a triangle given the coordinates of its vertices, and then simplifying the resulting ratio surely can't be that painful; this isn't how I'd approach the question if I needed the answer but it is almost completely routine). In fact I think there exists a rather general computational procedure for solving questions in Euclidean geometry which in principle renders all questions like this one routine.
But these "routine" solutions are long and tedious and boring, and no one (no one here, at least) actually solves these questions that way. So, in practice, solving them requires some cleverness, which makes them "puzzle" rather than mere "problem" according to the standards we have here.
I think there are fairly routine solutions to the hexagon question that aren't much more painful than the clever one currently posted there. So it's a bit of a borderline case.