Translation:What sports do you like?
Yeah, the S sound in ツ has nothing to do with the English plural, it's just a limitation of the Japanese syllabary. It's common to end a loan word with a character from the う column because the U sound is often dropped in pronunciation, but there's no character for "tu" in Japanese, so we have to use "tsu." You'll also see loan words that end in ト to avoid this problem.
There is a Japanese word: 運動 (うんどう undou), which means athletics, or movement. You can still see it used in words like 運動会 (うんどうかい undoukai) which means "sports festival" or "athletics meet", an annual event at most schools.
You can usually use both, but the は would make more sense only if you are talking in general and bringing up the topic. But you need to stop relating the が and は to certain sentences, I know this is easy but that's not how it really works.
If you are asking something particular, about someone's taste, you would use が because the focus of the sentence changes depending on the particle as well, in this case, the dynamic is that you are asking about "what sport" and not "whether he likes sports or not"「何のスポーツ←が好きですか？」and が throws that focus onto the element that's marked by it.
The context I do not know, but I can assume that the speaker is either making emphasis to know which sport in the mental list of the listener(depending on context) is the one he likes. I think examples are better for this.
Your friend tells you: We need to join a sports club, they only have baseball, volleyball, and basketball available... 何のスポーツ←が好きですか？ "which one [of those in particular] do you like?".
It can also work in a general sense, if you use が here it can also mean something like an expression of emphasis. Your friend has invited you to several different games in different sports and you say: Meh, it was ok, is not really that fun.. your friend is annoyed and says: well.. 何のスポーツ←が好きですか？
If you use は the focus goes to anything else that is not marked by は usually to the right of the sentence; If you use が then the focus is thrown into the element that's marked by が.
focus → ●
With は you are stating that the "what sports" part is the topic, and then implying that the rest of the sentence is what you are interested in. But you, as the speaker, only wanna know about the sports he likes, not whether he likes sports or not, then が makes more sense because the「何のスポーツが」part of the sentence is what's important to you as the one doing the question. does that make sense?
EDIT: added a small textual diagram.
Yes, people can like only one sport, but this is a question, so you keep the options open.
If you ask this in plural, "what sports do you like?", someone may answer with just one sport, but also three or even ten. If you ask it in singular, "what sport do you like?", it's as if you're limiting the listener's response to a single sport.
The point is there is no difference in Japanese between the singular and the plural. This means that the sentence can be correctly translated using either the singular or the plural. Currently both are accepted.
Without context all potential correct translations should be accepted. We don't need to guess a context or decide which potential sentence is "better".
何の is kinda like is own word, similar to どの. 何の【なんの】means what kind, what sort of...
there are some nouns that don't need の as in 何色【なにいろ】 but those are more like exceptions. A good way to see these is by pronunciation, if you pronounce 何 as なに is separated but if you hear なん・・ it goes with another thing as in 何で？
何の【なんの】is similar to "which" or "what", So for example "what sport do you like?"... The plural for sports in this exercise comes from english, in english saying what sport in singular sounds weird for americans.
どんな would mean "what type", "what kind", So if you ask "what kind of sports do you like?" the answer can be physical, aquatic, etc... rather than just saying the name of a sport.
I see. So, "donna" is "what kind of" and "nanino" is "which one."
Oh, also, "Which sport do you like" doesn't sound weird to Americans. being an American myself, I think I can speak with some authority on that. The major difference between "which sports do you like" and "which sport do you like" is based on what the speaker expects to hear. If the speaker thinks that the listener only likes one sport (or is asking for one out of a list), then he or she will use the singular. If they're asking for a list of sports that the listener likes, they'll use the plural. Though, it's probably more common to hear "Do you like sports?" and if that's answered affirmatively, then they'll ask "Oh, what kind?" And by that you kind of expect specific names (baseball, tennis, etc.) but it's also okay to answer it with things like "aquatic" or "winter sports." If the one who posed the question wants more detail, they'll ask for it if they get a vague answer.
Not that you never hear "What sports do you like" if the speaker just assumes you like sports at all. At that point you can answer in the same way as above, or clarify that you don't actually like sports. I think this sort of question is most likely to pop up if a relative older than you (particularly one who likes sports) is visiting and hasn't seen you in a while, like at a family reunion or something. Though, it's been my experience that it's more common to ask "Which sports do you like" rather than "What sports do you like."
"Which sport do you like" doesn't sound weird to Americans
yeah that sounds fine to me, but doesn't "what sport do you like?" in singular, sounds weird to you? that's more of a British way to say it as far as I know. "Which sport" sounds fine to me but "what sport" sounds weird, but that might just be me. What about "he's good at sport"? that one sounds really off to me, I would say "he's good at sports" instead.
And yeah, the english sentences are more general, I was explaining from a japanese meaning perspective. And btw, It's なんの as in nanno, not nanino.. here is a good article if you want to read more:
"What sport do you like" is still fine in American English, as I said. It doesn't sound weird to me, just a bit uncommon.
But for the other one, yeah, it would be "he's good at sports" or "he's good at a sport," (usually going on to specify which sport, specifically, he's good at) depending on if he's good at a particular sport, or just sports in general.
Also, I understood that you were explaining the Japanese sentence from a Japanese mindset, which I am very grateful for! I just thought that I could be helpful, too, in clarifying the American English prospective. It's not often that I get the chance to help someone out in that specific arena, and as I'm sure you know, it's very fulfilling to be helpful to someone else.
And on that note, thank you for the help! :) It's nice that someone can assist when someone else wants a deeper understanding than just "it's said this way because that's how it's said."