I am having a problem that I need to mouse-over a quote to see it. Is this a bug or intentional?
See in this link, I need to mouse-over "Royal Canadian Bandit" quotes to see them. Why does Poe Dameron leave Jakku without BB-8?
That's called spoilertagging.
People use it to mark content that could be seen as spoilers. E.g. in the answer you link to, people who haven't seen The Force Awakens might not want to mouse over those sections of the text and learn what happens in the film.
See also the various spoilers posts on meta, e.g. How should I be indicating a question is, by its very asking, a spoiler? and What is the policy for spoilers?
Because those are spoiler tags, not regular quotes.
If you look at the markdown of that post (by clicking the "edit" button) you'll see that Royal Canadian Bandit was using
>! instead of