Why is Quidditch always capitalized? Soccer isn't, football, baseball, basketball, etc. aren't. Why is Quidditch always capitalized?
I’m not sure this is really an answer as such, but it is at least an explanation, for what it’s worth (and MaxD suggested I turn my comment into an answer, so here goes).
The reason seems to be because J.K. Rowling.
For reasons known only to her (and/or her publishers, presumably), words that Rowling herself has invented and which pertain uniquely to the wizarding community are more or less consistently capitalised in the books. Words that exist in real-life, non-wizard English, on the other hand, are capitalised as normal.
Quidditch, being an invented word that pertains to the wizarding world only, is thus capitalised. The same goes for various other words, like Muggle, Butterbeer/Firewhisky, Chocolate Frog,1 and Remembrall. Also consistently capitalised are spells and various types of magic (like Apparition/Disapparition, Floo powder/network, Portkeys, Petrification, Horcrux, etc.), which after all also fit both the criteria of being invented and wizard-specific.
Conversely, similar but non-invented, non-wizard-specific words from similar categories are not capitalised: rugby, wizard/witch, mulled wine/ale, treacle fudge, and alarm (closest non-wizarding equivalent I can think of to a Remembrall that appears in the books).
That doesn’t tell us why Rowling (or her publishers) thought capitalising such words was a good idea; but it does at least allow us to state that it’s not just Quidditch being odd—it’s quite consistent and, at least from a certain viewpoint, not entirely nonsensical. There’s no real, pressing need to capitalise these words, but it does make them stand out from the surrounding text a bit more, which can be useful.
1 Of course, names of sweets are not unlikely to be trademarks, anyway, so all bets are off—the books also capitalise Mars bar and Bertie Bott’s Every Flavour Beans, both of which are more obviously trademarkish, the former being an actual registered trademark™. I suppose Butterbeer and Firewhisky could be trademarks, too, but they sound more like generic types of alcoholic beverages (Butterbeer clearly based on butterscotch).
It’s a bit unusual, isn’t it?
I can't think of a good rule in the English language that would cause it to be so. According to Quidditch through the Ages, the name comes from Queerditch Marsh, a place where an early forerunner to Quidditch was played:
So perhaps because it’s named after a real place, that elevates it to the status of a proper noun? (As opposed to, say, football.)
But being named after a real place doesn't entitle a sport to get a capital letter. For example, rugby is likewise named after a real place, but isn’t treated as a proper noun. And as @MattGutting points out in the comments, that was originally capitalised as "Rugby football", and has since lost its capital letter. Quidditch has been played since long before rugby.
Magical folk just have different grammar rules, I guess.
(Not sure answering about English is on-topic here, but the capital letter doesn't seem to have anything to do with the magical world or any hidden significance)
Quidditch is a proper noun. (Please have a look at this answer here).
So, as football, cricket, etc are not proper nouns; so they are not capitalized, unlike the case of Quidditch
Or a much exciting answer would be @AncalagonTheBlack's comment above:
"Quidditch" is not a proper common word in english (or in any another language like french), therefore it should be capitalized (or at least put in italic or between double quotes).
However, you would expect that in the magical word, they would have their own version of the english dictionary with lot of words not present in a muggle english dictionary; including the word "quidditch". Therefore, anyone with knowledge of the dictionaries of the magical world shouldn't capitalize this word; excerpt maybe when writing to a non-magical beeing such as a muggle.
This is clearly the case of the narrator of this story. While he as knowledge of the magical world, he is speaking to non-magical beeings, ie. the readers; therefore capitalizing it should be the correct way of writing it.
However, in certain situations like showing the extract of a newspaper or of a book known in the magical world, this word shouldn't be capitalized.
I believe Quidditch is more like a brand name.