Thomas Shey
Legend
I haven't run enough games set modern or near-future for it to usually be an issue, and the majority of those I have have been superhero games where its somewhat moot.
In my East Texas University game, one of our adventures started with someone trying to photocopy pages from a book written in Enochian (Angel-language), and for Mystic Reasons that resulted in (a) a blurry copy and (b) the Power of Creation held within those pages animating the photocopier in question (with a delay, so the person attacked by the animated photocopier was not the one trying to copy the book).In my games, magic/supernatural and tech don't really love each other. So all those mystic books, when scanned or photocopied or photographed, they miss something, something that's perceived only by human eye and brain directly reading from manuscript.
I think the closest I've gotten to a game set at the same time as we were playing was TORG back in the 90s. I got the game a few years after it was published, but that was close enough. The second closest is probably the aforementioned ETU game, set ~15 years in the past.I was trying to think of what I’ve run that was set in the “present day”. And I realized that I haven’t run or designed a campaign contemporaneous to IRL since the 1990s, or possibly the early 2000s. And all that I can remember of those is they were all supers games except for one martial arts campaign.
Everything else has been fantasy, a future at least 1000 years from now, or set 1970s at the latest.

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.