Disclaimer: Since I first posted my answer, there have been a few good answers and comments that have highlighted how the version labels may be useful. I feel that they have solid points, but I still stand by my views presented in here and have hopefully updated them to present my viewpoint better.
I feel it'd be a neutral change at best, and is far more likely to be detrimental.
To understand how these would affect us, lets look at the most useful scenarios for it (as indicated by the table):
We have questions without any edition tag on them, and people apply version labels to their answer in order to identify the associated edition.
This seems perfectly fine until you realize that the OP's question is coming from a specific edition, and that edition may not even have an answer in the question they asked for themselves. Additionally, this also leads to high amounts of duplicates questions being added, as questions that already exist don't have answers for other editions and questioners need to wait for answers to the central question to be posted instead of asking a new one.
If we then argue that questions should have the edition on them already, and thus questions asked for another edition aren't duplicates, then why would we need to apply a version label for the edition? All answers on that question should be for that specific edition in that case.
Not to mention how to handle things like pathfinder and blades-in-the-dark, which are based on a system, but are also their own system as well.
Additionally, something to remember is that a version label is not something required for an answer. If the answer is not based on a particular edition, or is general advice that's being given out, a version label shouldn't be applied to the answer.
However, if a new user is posting a new answer for a question, and every answer so far has had a version label, how likely do you think it is that they'll feel pressured into adding a version label, even though it may not be relevant or even apply? And if their answer gets sent to a review queue, is a reviewer likely to make the mistake of adding a label when one shouldn't be added?
So at best, it's a neutral change with a lot of work behind it, and likely it makes for a worse user experience while increasing the learning curve for a new user.
The ability of users to create versions.
Something else to note, is that the initial plan is only for versions to be rolled out to Gold Badge tag users and Moderators initially, before the requirements are slowly lowered. For systems like paranoia (an example used for where versions might be useful by another answer), they don't even have enough questions for anyone to qualify for a silver badge in the tag, let alone a gold badge, leaving the initial push of versions to heavily rely on moderators.
While the requirements may lower over time, the smaller systems that benefit the most from these version labels will have the hardest time creating them.
Editions are not the TTRPG equivalent of Versions.
That table is also misguided in thinking that the equivalent of versions for us are the various editions when they are not. Claiming that dnd-3.5e and dnd-5e are merely different versions of dungeons-and-dragons is like claiming that C++ and Lua are merely different versions of C. While there are similarities between them, and they do have relations to each other, they're wildly different and should be treated like two different programming languages or the two different systems they are.
"But Will, what's the TTRPG equivalent of versions then?" You ask. I'll tell you. It's books. Each and every book written for the same system is a version. It's a version that applies changes to the system or adds more content and capabilities to the original system.
So if we use version labels, they should be used for books. Not that we should use them anyways.
Now for some RPGs, their editions can be equivalent for software versions, but the same point about books being versions still applies, it just happens to be the rulebooks of the various editions rather than other books written for the system.
SilentAxe's idea of using versions for different settings in a system (such as dnd-5e) is a valid idea for their utilization as well (a very nice one, imo). However, this also lends more confusion about how versions should be created, as well as what constitutes a version or version range.
: I don't see this as a rather large issue, as we generally have pretty good crowd around here and mistakes can be caught quickly, but it is one of the multitude of smaller issues that version labels will bring, and I can practically guarantee it happening at least once.