I've linked this page because I'm considering re-opening this. It clearly fits within the guidelines attributed in the FAQ.
Is this okay?
I'm inclined to agree with you. I can't recall seeing anything in the FAQ, or on Meta, that would indicate that the question is off-topic.
If we're going to close one, we should close the others; or reopen the first one. To that effect, I've voted to reopen the first one.
Do I think it's a good question? Absolutely not. But, a close vote is not a super downvote.
Should this question have been closed as off-topic?
No, it is clearly within the scope of the site. Genre/terminology questions are perfectly acceptable according to our FAQ, and I'm not going to vote to re-close it as off-topic. Your example #2 is a great question.
Should this question have been re-opened?
No. Just because a question is closed for the wrong reason doesn't always mean it should be re-opened. Let's be honest here, some questions are just too simple. That's not the same as a legitimate question being easily answered on an easily searchable wiki. This question practically answers itself.
Lets look at the stats. As of this writing the question is well over 2 years old, has 1246 views, and has a score of -6. Now, the age and view count are not condemning in themsleves, but when paired with the score, we have to ask ourselves: What did we gain from re-opening this question?
My answer here is nothing. Let's look at some similar potential questions:
What genre do games like Gran Turismo and Need for Speed belong to?
I mean games where players race cars against each other.
What genre do games like Scribblenauts and Cut the Rope belong to?
I mean games where each level is a puzzle which must be solved.
Are those questions on topic? Yep, sure are. Should I go ask them? No. They are of zero use.
So the real question is, why are we rallying to re-open 2 year old garbage? Yes, a close vote is not a super downvote, but let's just use some common sense. Are we really better off having this question open? Who is it helping?
So what is to be done? If we leave it closed as off-topic when it isn't off topic, it will give the wrong impression about what is/isn't on-topic. Since this question is at -6, it should have just been deleted. Nobody would have missed it and we'd all be better off.