I believe that one who truly appreciates and loves the works of Tolkien is a fan of his. Setting requirements on who can be classified as such is both unproductive and unnecessary. I would say reading some of his works is a good start. Normally people have read the Hobbit and the Lord of the Rings, though having them as requirements makes little sense. Perhaps you like the Silmarillion, the Unfinished Tales, Roverandom, his scholarly works, his analysis of Beowulf. Maybe you haven’t read any of his works, although I would strongly advise you do so if you truly love his work. Yet even those who love the Peter Jackson movies, the animated film, the Shadow of Mordor/War games, or are excited for the Rings of Power are all welcome to the Tolkien fandom.

I have read lots of Tolkien’s works myself (not trying to sound superior) and yet I love to play the Shadow of Mordor/War games and I have always watched the LOTR films and enjoyed them (I know, I know they are corny at times). Call me a gatekeeper but perhaps the only qualification I would set is if someone respects the canonical and legendarium of Tolkien. How can you call yourself a fan of Tolkien if you only like the bits of lore invented by Peter Jackson. Besides that, go wild. Back to the Shadow of Mordor/War games, I like to feel I have a strong understanding of the general canon of Tolkien and yet I love those games. I have to mentally disconnect them the lore but besides that I genuinely love the atmosphere.

TLDR; gatekeeping bad, all are welcome. Enjoy Tolkien, love his works, and indulge in some pipe weed with your fellow Tolkien comrades.