Excellent question. It is optional to use the article with adverb superlatives, although using "the" is definitely more usual. Your example can be changed to include the article. "Which animal can run (the) fastest?" Your first example, however, used an adjective (tall) but it wasn't directly before a noun. Therefore, it becomes optional. Here are some examples: This muffin is (the) tastest. This is the tastest muffin. ("the" is mandatory in this case as the adjective is right before a noun)

"Tallest" and "fastest" are adverbs in your sentences. In "the tallest animal" tall is an adjective. Best wishes

I would say it's just nuance: If you're starting talking about all animals in the world, or a specific group, 'which animal is the fastest/tallest?' is good because THE fastest/tallest is very specific, however, continuing the conversation with more superlatives, there's no need to be as specific each time; 'And,.. which (of them) is fastest/tallest/cutest?, etc'. You can say THE each time, but it seems to emphasize that each is special.