The claim that Taylor Swift has publicly confirmed she's dating NFL player Travis Kelce is true, however, there is no documentation of Taylor admitting she's "in love with him." The two have been seen out together on numerous occasions, there are videos of Taylor going to Travis' games, and Travis has been seen attending her concerts which has gained lots of media attention.
Before Time magazine released their 2023 Person of the Year: Taylor Swift, she hadn't spoken on the matter. In the article, she explains how the two started dating, but never spoke on whether she loved him stating '"When you say a relationship is public, that means I’m going to see him do what he loves, we’re showing up for each other, other people are there and we don’t care,' she says. 'The opposite of that is you have to go to an extreme amount of effort to make sure no one knows that you’re seeing someone. And we’re just proud of each other.'"
The YouTube video itself didn't speak on their feelings for each other either; rather, they used a clickbait thumbnail that said "I'm in love with him" next to a picture of Taylor's face. They proceed to not address that quote at all. Mostly it was all based on speculation and quotes from anonymous sources close to the couple, which aren't always the most reliable. Moreover, the video is titled "Taylor Swift Finally Speaks On Her Relationship With Travis Kelce" and was posted by a gossip channel: Gossip Tea.
Overall, from my fact-checking, this claim seems to be false. The YouTube channel was also purposefully trying to deceive the viewer in order to get views.
Sources:
https://time.com/6342806/person-of-the-year-2023-taylor-swift/