Was there a RCT scenario when you had a compete with a rival park?
No, I've just looked through all the RCT 3 scenarios, and there isn't anything there. I'm also 99.9% positive (having played RCT1 and 2 for many years!) that there isn't anything in those as default campaigns.
I highly doubt there was a scenario like this. Programming AI is hard and they would not have spend the time for a single scenario. I can't remember something like this either. And the launching people into the rivals park seems ridiculous, not sure about the mechanics but you would think the dead's get count to the owner of the coaster where they died in.