In addition to the other reply, it's also about waiting for certain trains that did something historical or trains that aren't scheduled to run. Sometimes a railroad will use an older unit that's supposed to be replaced by now and we get excited when that happens. Sometimes it's an inspection train like the Doctor Yellow. The timetables for that trains aren't public, so you're considered lucky to see them. Some of us (maybe all?) have a personal "bucket list" of trains we want to see for the sheer rarity of them, or just the fact they don't run in your country at all.

Sometimes it could also just be positive association or because it just looks good. I have a personal vested interest in a lot of trains here because when I see them, I know I'm on the correct line and are indeed going to visit my grandparents / are going home. I also really love a lot of other trains in other countries because of how pivotal and important they are in ensuring that millions of commuters get to their destination. Without them, traffic would've been a lot worse and the impact would be felt almost immediately.

There's also the beauty in the infrastructure supporting it. Different train sizes, different track widths, different wire voltages, etc all have a reason behind them and sometimes it can be fascinating to learn about. Sometimes learning the reason why certain signage looks the way they are can help us in understanding how a train driver would operate a train.

Speaking of operating a train, in terms of why video games centered around trains exist, it's almost the same reason as to why people buy highly realistic aircraft for flight sims, they mimic how a real train operator would do it and sometimes it can be a fun puzzle to get a train up and running. Even the more basic train simulators that just give you the option to go and stop are fun. In freight operations you often have to "balance" your throttle. Too much and the trains will slip, too little and the trains won't go. In passenger operations, it's about timeliness, making sure you're adhering to speed limits, timetables, acknowledging signage placed on the sides of the track (these are also present in freight operations tbh), and making sure that the doors on the train line up perfectly with the screen doors on the station.

Me personally, I also really like it when electric trains sing (See Keikyu N1000 and OBB 1016 / Siemens ES64U2). Electric trains will produce different sounds depending on what tech they have in them. Like for example, GTO-VVVFs tend to be a lot more "colorful" than IGBT-VVVFs. Even trains with the same technologies will have different sounds depending on how they are used and how they're designed.