Well, I guess that means there's only one option left for us.
A Let's Play.
A succession game à la Dwarf Fortress, everyone takes the park one year and then they post how much growth they did get that year to see who's the better park manager.
Actually this sounds pretty cool. Someone should do this.
Hell, I might if no one else does.
Objectives in RCT2 differ from "have X guests in your park by date Y with park rating Z", "pay off your loan of XXk by the end of date Y", indeed the "build XX rollercoasters with rating Y by date Z" thing, "have park value of XXX by date Y" and a few things more.
But you can also make your own parks with objectives if you want to mess around, but I'm afraid that there's no free play mode.
All right, doesn't sound much different than the first game and its expansions. I'm fine without free play, actually, but I don't have the kind of brain that enjoys masterfully crafting rides with specific ratings. It's very restrictive feeling. The rest of the objectives are either fine or wonderful imho.
Building your own scenario is the closest thing to Free Play you can get, and it's pretty good honestly. However, the scenarios in RCT2 are pretty lame, whether vanilla or expansion. You won't find any scenario that makes you feel like this is something you can make something neat with, like Evergreen Parks; nor ones you can stare in awe at like Diamond Heights.
RCT2 is still better due to the landscaping options and other additions and you can download ports of RCT1 maps online.
Oh, and you can't charge for both parks and rides. Each scenario allows for charging of only one or the other. Charge extra for the restrooms to make up for that.