There is some precedent in reserving the "basic" tag for a set of editions for only questions that are about all or many editions. That precedent was set by our discussions about how to tag D&D questions though, and D&D being the 800 lb gorilla of RPGs, it is somewhat exceptional.
The advantage of avoiding the extra tag is so that more room is available for other tags that might be needed for the question. D&D being a widely-known set of game editions makes this feasible because most questions start with the understanding that they have to be about a specific edition, not just the non-specific “D&D”.
There's also precedent for tagging questions about smaller games / games that generate fewer questions with both a general tag and the game-specific tag (see Clean up tagging for "World of Darkness" related questions).
The advantage of this approach is that all the questions about a particular game's editions can be found easily under the general tag. This can be useful when editions are very similar and have points of compatibility, or when people interested in one edition are often interested in many or all editions (which happens more often when editions are very similar).
I think Traveller questions here fall into the second category: nearly always specifically about one game, but people who play one edition of Traveller seem to be interested in many other editions, as sources of ideas and rules to borrow. If that's the case, then I think we should tag with both traveller and the [game-specific-tag] when available, so that they can all be found under the traveller tag. In that case, just the traveller tag would mean either Classic or one of the other “old” editions, which we would have to see clearly indicated in the question.
However, that's now. If we see an influx of many Traveller questions — which we might, if the recent releases of Traveller 5 and Mongoose Traveller 2 instigate a renaissance in interest in the games — then we may want to avoid the “tag tax” of needing to include the general tag, as with our D&D tags. That would also free up the general traveller tag to mean something more specific, such as “questions relevant to most/all Traveller editions” or perhaps specifically GDW's 1977 Traveller (though in either case, we would need to make a new tag to represent the other one).
(A good heuristic for whether we might need to make that choice is if we get a lot of questions tagged traveller that don't bother saying what game they mean and turn out to not be Classic. That would indicate that how to choose among our Traveller tags is not obvious and that we need more specific, obvious tag names to help guide new askers.
This is actually how mongoose-traveller, mongoose-traveller-2, and traveller-5 came about: I noticed a small influx of questions that just assumed that readers would see “Traveller” and equate it with “current” Traveller (despite there being two-maybe-three). I knew we needed those three tags for fans of the recent Traveller games to pick, so they won't assume that saying “Traveller” means “obviously the current edition”.)
TL;DR: I think we should use both traveller and [game-specific-tag] where available, unless we see a sharp rise in the number of questions about Traveller games.