The easiest way might be to just skim through the actual entries of people searching the page for "non-human" and seeing the sorts of things people are watching for that category. :)
Not sure about lists but Kingdom and The Odd Family Zombie on Sale in your Plan to Watch list have zombies and The Tiger, obviously, has a tiger central to the whole story though it isn't humanized/is kept realistic from what I vaguely know of it. Tropical Malady (Thai film) also has some kind of tiger-related story arc but I couldn't tell you if it's central or just a momentary thing.
Vampires, ghosts, angels, demons/devils and other mythical creatures, robots (search for AI related tags, for instance-My Holo Love has a hologram program as a key character and plenty of AI robots are in Asian dramas), and of course animals if central to the plot count, too-I watched one with a cat as the main character this year and ; my 1980s one revolves around a dog: https://mydramalist.com/2491-hachiko-monogatari (or if you're into cats and want it more realistic https://mydramalist.com/25449-the-travelling-cat-chronicles -just beware they're Japanese and intend to make you cry); currently airing https://mydramalist.com/52995-the-story-of-gumiho features all sorts of mythical creatures including nine-tailed foxes, and searching for 'ghost' will no doubt bring you a lot of titles that feature them etc, as will vampire or robot/cyborg etc.
When searching, in addition to the title, if you "advanced filter->titles" on the left a third of the way down the page, try both the title (ghost, vampire, robot, goblin, cyborg, gumiho, fox, werewolf, devil, angel, etc) and use the "genre" (which has Animals, Vampires, Zombies, and Sci-Fi and Supernatural which will oftentimes have non-humans) and "themes/tags" if there's something specific you want to explore. (Just search w/one at a time in terms of genre/tag; you can choose other filters ie country, type [drama vs movie], year range etc, but the genres, tags etc give better results when limiting them.