The negatives to lying and faking outweigh any positives.
If you are in a workplace, it's especially damning. Stuff like that spreads quick, and if it reaches management, practically kills anyone of importance taking you seriously. You'll always be known as "that weirdo who lied about playing a video game" or something similar.
...what? You really think this? Like, seriously?
You think someone will get passed over for promotion because they lied about video games maybe once? "Well, we'd put Steve in a management position...but do you remember that one time he said that thing that wasn't true about Skyrim? Can't trust him to get the job done." Get out of here with this hyperbole.
Even then, you still have to make assumptions in these experiences. I mean, the person I quoted made the ASSUMPTION that the girl in question was maybe "trying to impress him" so "she lied". Where as a rational human might have just figured she was trying to find some common ground and maybe didn't know the system she was actually playing on, and only knew the name of the system she see's on TV all the time. I mean, I can't count the number of times my extended older family has referred to a PlayStation as a "Nintendo". I didn't take to Google to illustrate that they were, in fact, wrong...because that's petty and childish (just like that poster was being).
You can have your thread, it's totally fine, but trying to frame this as you correcting "bad behavior" is not a great look. At least accept it for what it is, and that's just you judging someone because they aren't as heavily invested in your hobby as you are.
It's not about feeling superior or embarrassing the other person. I would have probably said that "Um... actually Injustice 2 isn't on Switch". That's it. If saying someone is wrong about something is enough to make the person not want to talk to you, then I don't think that person would have been a good friend anyway.
And I'm not saying that you should start correcting everything you hear like you are on a holy crusade. I just don't think that correcting someone about an error that they have made is a horrible thing to do. If you start constantly correcting everyone, then I agree that you are being petty.
What is gained from that? I mean, particularly gained from pulling out your phone, going to google, and then showing someone that what they said is actually not accurate. Why the journey to hold them accountable for...misspeaking about a video game? It's entirely arbitrary, and doesn't change anything except for their perception of you. I mean, imagine going to a mechanic and saying "well, I think maybe it's a problem with the carburetor" and the mechanic then pulling out his phone to illustrate why you're wrong and that cars don't have carburetors anymore...instead of just understanding that maybe you don't have the same years of experience they do, and that you're doing your best to understand something foreign to you. Maybe just bringing up "well it may be your fuel injection system, sometimes you can get a blockage in there that can cause it to run poorly". No need to correct, just a small, passive teaching moment that shows you respect the person enough to at least have a conversation with them without having to be "right" (and have it KNOWN that you are right).
It's a ridiculous way to approach the situation, and does absolutely nothing beneficial for either party. In the end, they think you're a smug jerk (because that's how you acted when you pulled out a piece of technology to show them how ill informed they are to their face) and you feel better for a little while because you were right, but in the long run you just keep chasing away people who are different from you because you can't stand to see your hobby "defamed" with "filthy lies".
Sure, there are times to call people out for being wrong, but rest assured, they are considerably more rare than people would like to believe.