Oh yeah! That game!
Funny story: I actually owned these for the PSP instead of the console versions, but one of the things that immediately stuck out in my mind was the plot where Uncle Mortimer, who was this weird caricature of Doc Brown from Back to the Future, had hired you on to build this amazing theme park in the name of one-upping Globo-Joy, the competition, and it slowly devolves into corporate espionage to the point where you must destroy Globo-Joy from the inside out...BY BUILDING BIGGER, BETTER, AND MORE DANGEROUS THEME PARKS!
Screw brain cells, the more you ride, the more you build, the more we force them into bankruptcy! We got a treasure land park to make from your sorrow and pain, Mr. 'Vernon Garrison'"! Except the actual mini games over the rollercoasters were...a lot more fun. Despite the fact that the rollercoasters in both games had a first-person mode, IIRC...
And then you built, like, 5 parks, including a time machine themed one called...Thrillwarp? It's been awhile, and I'm going off the top of my head. Which was kind of a cool inside joke given Mortimer's look and voice, who was voice by Brian Greene. Don't know if it's the scientist Brian Greene, but it'd be cool if it was.
But then they just got rid of it in Off the Rails. Period. Which I get: nobody really went to RCT or Planet Coaster for stories, but at least Thrillville made up for the lacking coaster editor with a really weird story. Now it's just that you can take off tracks and kill people! ...Or you could, if they all didn't just have parachutes. The pansies.
But yeah, I sunk so many hours into the original on my PSP. Unfortunately, I don't have my PSP near me, but I will tell you it was a great portable experience, and I can only imagine how much better it would be on console. And now its sequel is also on Steam, so bonus for PC players.