Here's my speculation based on the audition materials.
Details were changed in the audition package in a fairly feeble attempt to keep the plot and characters obscured. This is common practice early in movie production.
Dexter is Rex. They already have an energetic, capable, wheelchair-using pup who lives with creatures away from civilization.
Martin is Marshall. He is feeling insecure because of his clumsiness, crashing his (fire) truck in the script snippet. Brunker and Barlen's writing style is to repeatedly have situations that highlight the core conflict of the main pup happening (suddenly everyone talks about Skye being small even though it was never brought up in movie 1). Thus movie 3 will be about Marshall messing up a lot but getting guidance from Rex about owning his mistakes and growing from them.
Winston is Rubble. When choosing a fake name for a bulldog, Winston is a popular choice because of association with Winston Churchill.
The Jungle Island is a dinosaur island and the "Jungle Animals" are dinosaurs.
Watermelon is likely a cute pet dinosaur mascot character original to the film, but there's next to no info to go on here.
Honestly, while I may be wrong, I think this is so obvious that I'm really surprised it's not the mainstream interpretation in fandom outside of certain anonymous discussion forums.
It seems incredibly unlikely to me they'd erase one wheelchair-using pup from the show to create another. They want to follow up superheroes with something big and striking. Is it more likely to be jungle animals or DINOSAURS? And when you read through the script thinking of Dexter as Rex (in a world where he hasn't had the Turbots), Martin as Marshall and Winston as Rubble, everything in my opinion immediately clicks.
I'm mostly making this post so that in a couple of years I can refer back to it to see how right or wrong I was.
