It probably is the best fun time kart racer* at present and that is just really depressing when I think about it.
I mentioned a few things I find fault with. The menus are where I would start -- it is almost unforgivable that I don't have the kinds of customisation that should be there, or indeed is there in the case of things like Smash Brothers (why can't I have a custom tournament of my own design, never mind tweaking variables). That lack of concern for game design carries over into other aspects. Worse is all the post double dash** (or maybe DS) ones I have played seem to be fairly aimless in their direction and just adding pointless features that do nothing to further gameplay and I would argue ultimately detract (coins, the transforming vehicles, bikes might have been something interesting but their implementation sucked, tricks have been interesting in the past in other games -- plenty of off road motorbike things seem to have good takes but fail for me here).
Back on the N64 and PS1 we saw other devs do things -- other than the stupid hub world and boss gated stuff I have long maintained Diddy Kong racing on the N64 as superior to Mario Kart. Lego Racers and some of the Crash Team racing games being other examples from things around that time which did really well. Sadly this desire to better the concept seems to have vanished or forgotten and we are back with weak clones. As far as "invented the genre" then I am not sure what to say there. In a very strict technical sense then maybe, however look at any of the "race to the horizon" games from the C64 on up and many arcade games of similar eras*** and I would say it was obvious.
*pauses to remember fondly
**by no means a game I am also not prepared to criticise at length as well.
***Not so many recall it today but Super Off Road was highly influential for its time, bit light on direct weapons but pickups very much being a thing
Similarly take a look at 1991's (mid-late 1992 being the date for Mario Kart on the SNES) Road Rash, which is another massively popular series that has been somewhat forgotten, and tell me that turning it into a closed track is not an obvious move.
Also Micro machines (though the sequels are probably a more obvious comparison, whether they lifted it from Mario Kart I do not know).
I will spare videos but see also Spy Hunter and Chase HQ want to be mentioned in this.
In terms of a direct thing I can point at and say this did Mario Kart style first (similar to how I might compare the 1994 Street Racer game) beforehand I am at something of a loss, again though I maintain it was an obvious direction to head in.