The relevant feature of Dyneema is specifically that its Young's modulus is much higher than most other organic fibers, about half that of steel, which is probably what you mean by "neither material has much elasticity".

Steel cables would work just as well if weight isn't a consideration, but I think Dyneema is likely to be more resistant to abrasion. However, heat produced by any significant dynamic friction will ruin it immediately, as I found to my sorrow. Kevlar is much more heat-resistant, and of course steel is more heat-resistant than Kevlar.

He actually used steel cables for his initial prototypes, but steel cables have a problem with rolling fatigue that actually gets worse the larger the diameter...so if a tiny steel cable is not strong enough, you might actually have to change the gear dimensions (and therefore ratios) in order to not fatigue them.

Dyneema is much easier to work with, too.

I'm quite fond of bowstring as a material for this sort of thing. It usually has other fibres mixed in with it so it's a little more bouncy than raw dyneema but that's minimised if you get thread that's intended for crossbows. It's usually waxed so there's some friction to it when you're manipulating it, and it's also easy to source.