I'm the guy who removed those tags, and you've got a great question about tag wikis. First, though, a clarifying point which will come back to be relevant to the topic at hand: I'm not an appointed administrator or moderator. Stack Exchange expects its citizens to help moderate the site with tools gained via participation (measured by reputation). You've unlocked a few of those already! Anyway, my edits aren't binding or magically correct, just my own best attempts to help out.
Now to your main question, about tags and their wikis.
Tags are a means of connecting experts with questions they will be able to answer by sorting questions into specific, well-defined categories.
Tags can also be used to help you identify questions that are interesting or relevant to you. [source]
This means that tags should be related to the primary drive of the question; nearly every question on the whole site could be tagged players, but very few would be usefully defined by that tag, which would render the players tag useless and pointless. A lot of questions do only have a single tag (usually a system tag like dnd-4e) because there isn't any other tag which could usefully be applied to them. (Maybe one needs to be made; see below.)
As for tagging to indicate the kind of answer you want to get--it's something we're still working the bugs out of, and you stumbled over it in the meantime. That's the other thing about tags: they're "emergent," meaning that we don't make them up in anticipation of a need, we make them when the need emerges.
This is very important to the site's health and dynamics for a number of experience-based reasons, but it also relates directly to your concern about tag wikis: tag definitions don't appear automagically, somebody has to write them. When a tag wiki looks weak (or doesn't exist at all), it's waiting for someone to write it or improve it. That somebody could be you!
All registered users can submit edits for tag wikis (until you hit a certain rep threshold the edits have to be approved by other users before they go public, but you get bonus rep every time that happens!). It's not something a lot of our citizens are necessarily really active in doing (I'm guilty of that myself), partly because system-specific tag wikis need experts in that system, while system-agnostic tag wikis need to be kept general enough that they apply to multiple systems without being so vague that they don't define anything useful.
Many of our tag wikis are, as you've noticed, sadly bare. This is a challenge we should rise to! Thanks for reminding us of it, and I hope you'll be part of the effort to improve our tag wikis. It's part of the whole Stack Exchange ethos, where all citizens work to improve the site behind the scenes as well as by creating front-page content.