It's interesting how I heard about M.A.R. Barker from his linguistics research first (he's a great resource on the Klamath language) and only later heard about Tékumel from a linked post in a thread here (in the Lands of Red and Gold thread). He was associated with contemporary linguists like Victor Golla, a notable scholar on indigenous Californian languages. If Barker and Tolkien are reversed, I'd imagine many interested in Germanic legend, language, or culture would know of Tolkien from his works in that field. Tolkien would be like the Brothers Grimm--LOTR would be his legacy, but he'd just as much be remembered for his Germanic philology.
Considering that the first Tékumel book came out in '85, the popularity of this fictional universe would co-incide with the Soviet occupation of Afghanistan, and the Western idolisation of the Islamic resistance fighters. If the books really hit the public mind-set at just the right time, this could be enough to actually influence foreign policy after the Cold War. Shortly after the Cold War, Bin Laden was regarded as a hero in the American press. If relations are better... that could butterfly quite a few things. The '90s as a period of Islamophilia in the West, with funding for Islamic insurgents opposing dictators being quite popular? Anti-Americanism among Islamists ameliorated and in some cases outright prevented? 9/11 completely prevented? No War on Terror?
Red Dawn was basically Hollywood's take on the Soviet War in Afghanistan and reading between the lines was very much trying to promote the Afghan struggle to American audiences (look how the heroes pose in the movie). But I don't think John Milius managed to influence foreign policy much with that movie despite its fame.
See Magi the labiryth of magic for a japanese example too
I suppose TTL might have Record of Lodoss War be instead more like Tékumel instead of D&D. But speaking of Japanese fantasy, I wonder if Yoshiki Tanaka, best known for
Legend of Galactic Heroes, writes
Arslan Senki (aka
Heroic Legend of Arslan) earlier or otherwise those books are more popular in ATL Japan and
Arslan Senki gets the lengthy anime adaption and the cult fame in both Japan and the West instead of LOGH (which would have the
My Conquest is the Sea of Stars movie and maybe an OVA of the first arc or so). So TTL might have a lengthy late 80s/90s adaption of
Arslan Senki perhaps done like the OTL OVA version and with the same fantastic cast. I'd imagine the OVA would have some divergences from the novels and some filler arcs which might still be received favourably, especially amongst Western fans if we imagine the quality is good enough to attract the same cult fanbase as LOGH.
I guess that means the TV version of
Arslan Senki from the 10s TTL would be like the 10s TV remake of LOGH. Personally, I like both versions of
Heroic Legend of Arslan since the remake is cheesy fun and is almost like an anime version of the Peter Jackson Lord of the Rings trilogy, although perhaps TTL it's more unfavourably compared to the original like the LOGH remake OTL and like said remake is often considered totally redundant to the original. Which would be too bad since I love the remake's take on Silver Mask and Marzban Daryun, although maybe TTL's remake isn't as good, and TTL's LOGH TV remake competes well with the original OVAs.
Aside from that (and perhaps most importantly), TTL's
Final Fantasy would have more of a Middle Eastern theme since the first
Final Fantasy was very inspired by D&D. Although perhaps the most important thing would be whatever happens with TTL's equivalent of
Wizardry since that early RPG was hugely popular in Japan (far more than in its homeland the US) and the godfather of all JRPGs.
I don't really like this take because it implies Westerners have to be ignorant of other cultures or that they're incapable of understanding other cultures. I find this view patronizing.
You only have to look at popular culture OTL to see generic Hollywood takes on all sorts of non-Western cultures. Hell, a lot of fantasy in general is that sort of Hollywood take on European culture via osmosis from Tolkien.