Other than gelatin what makes gummy bears chewy?

From a package:

corn syrup, sucrose, gelatin, citric acid, apple juice concentrate, sodium citrate, coconut oil, natural and artificial flavors, carnauba wax, red 40, yellow 5, blue 1

Likely the sugar types and their ratio is important. pH (citrate) shouldn't make a lot of difference unless you're using something weird instead of apple juice. Carnauba wax is likely a mold release agent, which leaves coconut oil as the most mysterious ingredient. I wouldn't bet on it affecting chewiness much, but these dense gel recipes can be pretty sensitive to minor ingredients.

I doubt that your ingredients are wrong, a wrong process is the more likely culprit.

Gummi bears are traditionally make gummylike with gelatine, nothing else. But what you describe as "springy" gelatine reminds me of the way gelatine becomes in its usual application for producing pie fillings and other desserts meant to eat with a spoon or fork.

Gummy bears are much drier than these desserts. I don't know if they make them that way by using more concentrated gelatine, by drying them out somehow, or both. But I think this is the main difference to a "classic" gelatine recipe. And as Wayfaring stranger mentioned, there are no other gelling agents in the mix of commercial gummy bears either.

One gummy bear hacker says you need to leave them out for 3 days to aerate for the gelatin to toughen up. The longer you leave them out, the chewier they become. https://topsecretrecipes.com/foodhackerblog/haribo-gold-bears-gummy-candy/