I’ve had the shot at that bar, and it was fine. Note that I love bitter and herbal drinks, like Underberg, Unicum, Fernet, Amaros, etc.
I unironically like Malort, but see above. Bitter flavors are in my wheelhouse when it comes to alcoholic tipples. It doesn’t taste much at all like absinthe, despite the wormwood. Absinthe is more about the anise flavors, really, with a wormwood backbone. If you’ve never had wormwood before, it is extremely bitter. The gentian in Moxie or the quinine in tonic water is in that general ballpark, but think of a drink that is exclusively composed of that bitter. Malort is a bit one-dimensional in that regard, but I still like it. It reminds me of a Polish drink called piłonówka, which is a drink of wormwood macerated in alcohol. The difference, I believe, is that Malort is not macerated, but distilled.
The first time I gave my father Malört, he loved it. The local newfound popularity with the drink came about sometime in the mid 2000s, to my memory. It was otherwise known as an old man’s drink, I assume probably popular with the more Central and Eastern European immigrant set, but that is conjecture on my part. Then it did become some sort of “dare” drink or rite of passage, or even a test of one’s “Chicago-ness.”
In the early 2010s, at least, there was a “hipster” version of Malört that was distilled in New York. I can’t seem to find reference to it anymore, so I assume that venture failed, but I remember buying a bottle and it was more interesting than Jeppson’s (which isn’t really hard to do.)
As to add to the OP and not just make this all about malört, if non-alcoholic drinks are allowed (and you mention Moxie, so I guess they are), Buffalo’s local quirk is loganberry drink. It’s just a very sweet , non carbonated red drink flavored with loganberries (a blackberry-raspberry hybrid.) Featured in many (most?) soda fountains across the Buffalo area. (And there’s canned versions, too, though I’ve only had it from the fountain.)