Is there always a new design for some Dinosaurs in Jurassic Park (games)

Depends. If it has an official canon design that's featured in the movies, then the games automatically use it. Dinosaurs that don't have official movie designs will have a variety of different appearances depending on what game they're featured in, like the Troodons from Jurassic Park: The Game looking completely different from the Troodons in Jurassic World Evolution. Giganotosaurus wasn't an established creature in the canon when the first Jurassic World Evolution was released, but now that it's been featured in Dominion with a different design, future appearances in media will use automatically use that design.

The Allosaurus, Baryonyx, Dimorphodon, Ankylosaurus and Carnotaurus were completely different looking back during The Lost World PS1 days.

Same goes for pre-Lost World, Compsognathus and Pteranodon from Jurassic Park (Sega Genesis)

Baryonyx deserved better

The Lost World: Jurassic Park for the Playstation 1 was the first time I knew about Baryonyx

Not to mention all the dinosaurs on Jurassic Park: Warpath and then you have the non-canon toylines