I can't really agree with this. I don't believe you can just say you are a fan of something and thus be a fan. The proof is in the pudding.
I can say I'm a can of Cheese Whiz or an Abominable Snowman, but as much as I say I am, I am clearly not. As much as some people hate it, this applies to more abstract things as well, like 'being a fan' of something. You cannot be a fan of something just because you like it. It's a bit more than that.
Merriam-Webster defines the word fan as 'an enthusiastic devotee (as of a sporting event or a performing art) usually as a spectator' and 'an ardent admirer or enthusiast (as of a celebrity or a pursuit)'. You'll notice something here, and that is terms like 'enthusiastic' or 'ardent', which can be connected zealous, fervent...or, what I like to call, 'OOMPH!' Being a fan means that you bring that 'OOMPH!' to whatever it is you like. You don't just say 'Yeah, I kinda like this show...I guess I'm a fan'; you would be more likely to say 'Dude, I am a HUGE fan of this show, we HAVE to watch this together. You won't BELIEVE how awesome it is!' There is a reason why the word fan spawns from fanatic...
Let me give you a better explanation in my own terms: investment.
Have you ever noticed that when you kind of like something you really couldn't care one way or they other about what happens, but when you are a FAN you occasionally go a bit to far with how you feel? That's the difference between something that matters and something that doesn't; that is the difference investment makes.
Take for example Game of Thrones. Someone who merely likes GoT wouldn't care too much about Season 8 being garbage. 'Eh, they could have done better here or there I think, but it is what it is.' Does that sound like a fan to you? Or do all the videos and posts on social media going absolutely ballistic and picking apart all the issues and being upset at the writers sound like fans to you? Sure, they may have responded in ways you think were going too far, but they did that BECAUSE THEY WERE FANS. They didn't merely like GoT: it was their favorite show that they talked about with their friends every day. They scheduled their time around watching the new episodes and even re-watching old ones. They named children after the characters. They bought merchandise and followed the cast on social media and...I think my point has been made.
To make this more personal, I found this mobile game recently. It's called Dungeon Tales or something like that. Discount Slay the Spires clone. I played it for a while for a day or two and mentioned it to a buddy of mine who likes deck building games, but I've already taken extended breaks from it to do other things. It's fun, and I like it, but I wouldn't say I'm a Dungeon Tales fan.
...But SMRPG tho?
I mean, look where I am right now! I'm spending time on a forum talking with other people across the states and even the globe who love a singular character from a 23-yr-old game! I listen to the soundtrack frequently and I have a playlist I built dedicated to remixes after already having probably 15 of them in my Favorites on YT. I've livestreamed the game and I play it occasionally even when I don't truly own it but I want to buy a SNES Classic/Switch purely to be able to PLAY the game legitimately. Jesus, I HUM THE MUSIC AT WORK AND IN MY DAILY LIFE! If I could easily find merch I would buy it now that I'm employed (speaking of which, anyone have a link for the Geno Blast shirt from way back? I still want it) and one of my biggest wishes if for Geno to get in Smash, so big that if/when it happens I could actually never ask for anything more from Sakurai ever for the rest of my existence!
Yeah, there is a reason why there are phrases such as 'you aren't a true fan' and the like. Sure, you can be a fan in your own way and you can even be a fan of only a portion of something and not all of it, but you aren't a fan just because you declare it. It will show in your actions.