I have to agree with what has been said above. If it's pulled off, it could be a really cool boon to the story. If it's not, it can come across as a huge drag. Some people like politics injected into everything, others really hate it. Your mileage may vary.
A good middle-ground if you can get away from it is lore injections into the story (provided they aren't too much exposition). People tend to like seeing deeper into a realized setting. You can easily allude to real-life events but through a heavily filtered lens within the story universe. You don't have to mention the assassination of JFK directly, as an example, but make something similar in the setting that readers can use that as a touchstone in real life. Using the idea of tabletop RPGs, the assassination of Dunkelzahn from Shadowrun was very much a hearkening back to the JFK thing. Even though Dunkie was a dragon.
I also got summoned to this thread by the mention of another tabletop RPG as inspiration. You just had to mention the World of Darkness didn't you... (I'm a old gamer, and a former freelancer of those games.)
The World of Darkness thing doesn't quite work. On paper, yes, a lot of the developers said they were against mixing real-world events with the fictional stuff in the games. In reality, they did it in spades. I remember how much yelling Justin Achilli did when New York by Night came out for V:tM right after 9/11 happened (the book came out just a month before the event, but submissions for new projects came out right after). Every freelancer was trying to get a plot-line in to mention the Assamites in New York, or how it influenced their involvement with the Camarilla. I still remember all the FULL CAPS emails to this day.
At the same time however, they dumped so much real-world stuff into the game it made the developers look like total hypocrites. The nuclear testing that India was doing, well that got included in the 1998-1999 Time of Thin Blood meta-plot. A virus outbreak that happened in Quebec around 2001, got included as a plot-line in Hunter: the Reckoning as a zombie outbreak. All of the little details about Pentex and it's subsidiaries from Werewolf were all based on real-world corporations, real-world groups, and real-world personalities. That time George Soros broke the bank of England, well it's mentioned in the Syndicates book for Mage. The NSA data-mining stuff in the early internet and FBI's Project Carnivore, that's all in Guide to the Technocracy. For the more outlandish stuff, they even tapped some of the rumors flying around about Project Solarwarden (old DARPA conspiracy) and used that for the Void Engineers. Also there's the constant mentioning of Rasputin in like every splatbook for the game (seriously, I have the full printed library in my office, you'd be surprised. It used to be an old drinking game).
Don't even get me started on the historical settings for OWoD either... Vampire: the Dark Ages, Vampire: Victorian Age, Werewolf: the Wild West, Mage: Sorcerer's Crusade, Wraith: the Great War (hell, even the Charnel Houses of Europe: Shoah sourcebook on the holocaust from Wraith, that was Rich Dansky's favorite project) and the revised Dark Ages line are -heavy- with historical influence and bias.
A good example of WW getting away with these kinds of in-world allusions to reality was HunterNet in Hunter: the Reckoning and SchreckNet from Vampire.
I don't know how much of a gamer Wildbow is, and if he's ever gotten involved in the WoD games, but you can see some influence in his work with Worm and Ward. It's not far-fetched that his in-universe inserts were inspired by HunterNet and the forum posts from the Aberrant game line (they are supers, after all).
As far as the newer World of Darkness stuff (NWoD and the new V:tM 5th Edition stuff). They are as political as all-get-out. If you've seen the latest beta for V:tM 5E, it has anti-trump stuff in it, antifa, EU politics, you name it. It's steeped in that stuff. Because the newer developers are hardcore punks. Even the NWoD stuff from Onyx is slowly starting to get way more political after Chronicles of Darkness came out (just take a gander at Beast: the Tumblring... I mean, Beast: the Primordial).
If you can make it work and do a fresh take on it. Do it. It'll be awesome. If you have some hesitation about it or see yourself being too political or heavy-handed with it, hold out from it and just work on your world-building a bit more. Use it for creativity and storytelling, not to beat people with a truncheon from a soapbox (we have enough of that going on right now).
Oh, and a nod to the OP here... Thank you for mentioning Call of Cthulhu <3
I just lost 3 SAN for posting here.