As usual with trademarks, the key question is "will reasonable people be confused about the source or affiliations of the product or service".
Trademarks are, as you already know, limited to a particular industry or area of business, in general. Displaying user videos is not exactly the same thing as a particular popular song, but they just might be close enough for some consumer confusion tom occur. Whether reasonable people are in fact confused into thinking that the app is in some way sponsored by the makers of the song is a question of fact. A trademark suit would probably need to present some sort of evidence that confusion had occurred or was likely.
It also may make a difference whether "Tik Tok" has been registered as a trademark. In the US, registration gets greater protection than mere use. (In some countries there is no protection without registration.)
It is also possible that the app has already licensed the rights to the term from the trademark owner for the song. This would avoid a potential suit.
It is also worth noting that the term "Tik Tok" is not original with the song. It dates back, in that spelling, to at least the "Oz" books by L. Frank Baum and others Tik-Tok of Oz dates from 1914, and the character of the Tik-Tok from the book Ozma of Oz (1907). Terms that are not original coinages are less strongly protected in trademark law, and the app could claim to be alluding to the Oz character, not the more recent song.
A comment by ub3rst4r says that:
the term "Tik Tok" is registered as a trademark in the USA by "Bytedance Ltd" (which is the company that operates the app).
If that is correct, the US Patent and Trademark office (PTO) came to at least a preliminary conclusion that this trademark did not infringe anyone else's trademark. That doesn't meant that an infringement suit is doomed, but it would make any such suit harder and less likely.
It seems that, as described in this news story a company selling watchs under the name "Tic Tok" was sent a cease and desist letter on behalf of the singer Kesha Sebert. The firm responded by filing a suit for a declaratory judgement. The case is Wimo Labs LLC v. Kesha Sebert, U.S. District Court for the Northern District of Illinois, No. 1:11-cv-02978. However, google does not show any resolution of this case, one way or the other. This was brought to my attention in a comment by StephanS. As this docket record shows, the case was dismissed by agreement without prejudice, apparently after a settlement (as stated in the comment by user muru). Thus there was no ruling on the merits of the case.
