I think you're probably asking for someone to explain the lure of NFTs. As for NFTs in general, I cannot explain the lure of owning some pixelated image or a weird ape picture. I can only speak to topshots which I do like.
1) Why do I want to buy it when I can look it up on youtube?
Because its a collectible. Why do people buy baseball cards when they could just print out a picture of the player on a piece of cardboard and print out their stats on the back. Why do people pay hundreds of dollars for a 1955 penny when it can only be used as $0.01 of currency? The answer varies from person to person for collectible to collectible, but the general answer has to do with it just being something to collect, there being a community of people who also view it as something to collect, there being some scarcity associated with the collectible, and I think oftentimes some either utility (like magic cards) or memory-evoking ability (baseball cards, coins) of the collectible.
2) It feels like we're going back in time
I think very much the opposite. I collected baseball cards as a kid. If I wanted to trade baseball cards with someone (which I did as a kid), I had to bring my baseball cards with me and was limited to trading them with people I interacted with in the physical world.
As the years passed, ebay became a place people could buy/sell cards to people across the world. You could find interested parties, send payment, and trust that the seller would pack and ship the card to send you to arrive in some # of days.
With Topshot, you have that same access to a world of collectors as ebay, but a much more streamlined marketplace and also there is no time or trust concerns. The NFTs are all stored and collected on the blockchain and the transfer of payment and the "card" are instantly taken care of with the click of a button.
My memory isn't the best, so I really like collecting these topshot moments to help me remember some good times of being a Celtic fan. This $2 Tacko Fall play is one of my favorites, which I can remember where I was and my reaction when watching it, which probably would fade from my mind if it wasn't for owning the topshot of it.
https://nbatopshot.com/moment/Action781+e9326376-20b0-41a8-86c8-f7e1f526deb9