To expand on what Wipqozn states: Autogenerating tags sounds like a good idea in theory, but the practicalities of implementing this would mean a lot of work for very little (if any) gain.
Where would this automated tag generation system pull it's list of games? Who maintains the list of games? Anything built by SE that pulls stuff from say Wikipedia, or PSN/Steam/XBL/Switch services etc would no doubt need a few handshakes, written contracts and months of effort to integrate with their systems. That's a whole lot of cost and effort for a problem that only occurs a) Once per game, when b) the asker is under 300 rep, and c) is the first to ask a question.
That's a very small subset of the community that gets affected. Is it worth going to all that effort for the couple of times this happens per year?
Even if this was still an onerous burden, there are probably other ways we could solve it, such as replacing the reputation requirement with a review system for new tags (similar to Suggested Edits). I'm not saying that this is a perfect solution either, just a lot less effort and more potential gain.
It's also worth noting that our community's workaround to this issue is codified in our faq question:
I want to ask a question about a game which has no tag yet, how should I tag it?:
State the game name clearly in your title and question body.
In the meantime, put some tags that do exist: platform, genre, and any other related items. You don't need to be obnoxious with a loud "PLEASE TAG THIS", just having the game name is often sufficient: often times that the people who can retag very easily notice when a question about a game has the platform and genre tags but not the game title, and will spring into action and retag the question appropriately.
If noone has edited your post with the game tag in a couple of days, you can ask someone in chat, or flag your post for moderator attention, with a custom reason asking for the tag to be created.