Right on the nose! It's the furious climax of this furious sonata (which I know as "Minacciosa", though I've heard the French also), whose very modern sound shows that even the monk-like Medtner was not impervious to the sounds his contemporaries were making. Of course, in his inimitable style, he then goes and pairs it with the deliberately provocatively titled "Sonata Romantica." Off the top of my head, a few other cases where outside cultural influences found their way into Medtner's music: the Op. 26 #3 Skazka has some jazz-inspired chord progressions (though they're not written at all jazzily), and Op. 38 #2 and Op. 54 #6 are ragtime in everything but name. Doubtless there are other examples. Someday I'll do a full writeup.
Let's summarize what we know about the remaining pieces, and throw in a few hints:
1 is by a European fellow who shared some aesthetic sympathies with Medtner (I believe they met, or at least corresponded by letter), though this guy wrote rather more floridly. Extremely colorful and detailed figurations.
3 is Medtner. But which piece?
4 is by an American fellow. Don't know too much about him but it's not surprising that this piece is from the 1920s.
8 is Alkan. Which?
10 is by an Australian who later became a music educator in New York.
13 is by a Russian contemporary of Medtner's who similarly had a rough go of things due to politics and a so-called outdated Romantic idiom. This guy is not in the same league but wrote charming works which deserve to be heard. I've seen his name mentioned on the forum before.
14 is by a gent who wrote intricate polyphonic music, both original and derivative works. Some of the latter have been criticized as disrespectful to the originals, but are increasingly appreciated by connoisseurs.
18 is Medtner (from an opus mentioned in this post). Which?
19 is Kapustin. Which?
20 is by an American who later became a music educator in New York.
22 is indeed Alkan. Which?
23 is by a Russian fellow esteemed for his otherworldly playing of Scriabin and Bach and loved for his teaching.
25 is by a rare Russian fellow who liked Wagner.
26 is by an Eastern European admirer of Brahms. His grandson is a highly regarded conductor.