Do we want to have questions tagged with the skill level of the person asking it, so others can answer with that audience in mind? I know it's a bit tricky, since we want to give definitive answers, but the playing strength really does affect the answer that will be most helpful.
For those who don't know me, I'm Grace Note, a Community Coordinator at Stack Exchange.
Tagging by skill level a different scale and system than normal tagging. Normal tags are designed to categorize what a question is about, not what a question is. That is, if you look at the tags of a question, you'd be able to understand what the question is covering. So, if there was a question tagged end-game, then it's pretty clear that the question revolves around the end-game of the match.
When you tag by skill level of the asker, let's say beginner, then that doesn't actually tell you what the question is about. It gives you warning that the user might not know the high level stuff, but nothing about the topic. For further reading on these kind of tags, this blog article touches the subject primarily.
The ultimate goal of the site is to help everyone at large, not just the original asker - that's why our focus is on the content. Treat the question as independent of the asker's skill level - you want to help as many people who have the same question as possible. These future readers could be of any skill level, so it shouldn't be branded to only a specific section just because the first person to come out with the question. If the asker's skill level is relevant, this should be made clear in the question body. Otherwise, answerers should be aiming to make their answers as universally helpful as possible.
Now, you could judge by the skill level of a particular strategy, perhaps. I admit that I'm not an excellent chess player, so I don't know if strategies are particularly divided by skill level. But in that case, you'd still be creating a meaningful classification of questions based on their content. You can group "high level strategy" questions because they're part of some set of high level strategy. But grouping by asker's skill level ends up pretty arbitrary and could span the spectrum of possible topics, rendering it very weak as a filter.