How do I quickly describe the timeframe a topic became relevant?
Ah, finding citations to back up generalizations. I know that annoyance, and I'm glad you're alert to it. When I'm editing my writing and find something like this, here's my thought process:


Do I really need to establish this time frame in the first place? If I can delete this part without negatively affecting my argument, all the better.
What would a really picky person respond and how do I deal with that? ("Actually, video games have been relevant since Pong!" "OK, I should narrow my claim substantially...")
Who would have written about this authoritatively in a way I can reference or quote? (For instance, look for a review article on video games in academia: someone reviewing the field systematically or a long-term contributor to the field could say the same thing with more gravitas.) 
Is there systematic evidence I could use, such as the founding dates of academic journals that are specifically about video games? (Perhaps the first issue editor's note would say something relevant.)
What examples am I thinking of? How can I reference them without claiming to be comprehensive?  E.g. "Video games were used in academic studies on computer graphics (see Mario 1987 and Luigi 1993), but it was a major breakthrough when articles began dealing with video games as an art form (e.g. SuperMeatBoy 2013)." 




More generally, timeline statements should usually be deleted out in the editing process. 

It bugs me when my students make historical-ish claims without having a true historical perspective. ("Nowadays, computers are more and more important!") These usually happen in introductions, where people are getting warmed up writing about the topic. 

"History" is rarely an interesting hook for a paper introduction, unless the whole thing is a nuanced historical analysis or there are interesting anecdotes that highlight a contrast. ("When Don Knuth began working with computers, it was standard practice to X (Knuth p. XYZ). Even though today computer scientists often do Y, implementing X in an object-oriented programming language can help us understand [topic].")