In another 10 to 20 years that won't matter with Moore's law slowing down. Globally competitive foundaries are one of the CCP's goals, and the same slow down that let TSMC surpase Intel will let some Chinese foundary surpass or equal TSMC. Their competitive edge is going to erode away to commodification (albeit for those who can stomach.the huge capital investment).
TSMC has never been very competitive with Intel. Intel has long been a leader in semiconductor manufacturing, but they almost exclusively used it for making their own chips; they weren't a contract fab. TSMC, on the other hand, has always been a contract manufacturer.
Recently the story has been TSMC is pulling ahead of intel in process nodes and intel has been missing deadlines, but this inversion has only happened in the last few years.
Basically, no, it doesn't (unless something has changed a lot since I worked there; I haven't kept up very much since then). Intel designs and makes their own chips, so they don't want or need a contract manufacturer.
This is like saying Ford's factories have no competitors, and that's true too. Ford isn't going to farm out their car manufacturing to some other company. (I mean the final assembly; of course carmakers routinely get various components from suppliers, such as airbags, infotainment computers, seats, etc.)
Chipmaking is a little weird because, unlike carmaking where the automakers all own and operate their own final-assembly factories, or aircraft makers like Boeing which own their own factories, chipmakers are frequently "fabless" these days and do the design work but partner with a fab like TSMC to actually make the chips. Intel is an exception and doesn't do this.
Just because they're vertically integrated doesn't mean they don't have competition, just that it's difficult to judge one half of the business on its own.
Intel's own messaging in this regard refers to the competition.
Ok, that's about Intel's "custom fab" business, which would indeed compete with TSMC. When I was there, that didn't exist AFAIK, they just made their own chips, so I wasn't aware of this (as I said, I haven't kept up much with that company since I left).