Doesn't regulatory arbitrage mean following the regulations but taking advantage of loopholes in them? So it's not illegal. That seems a bit different from breaking them, possibly paying a fine, and still profiting anyway. The latter is what I've heard of Uber doing in some cases. It's also what shops do by trading on holidays where they're supposed to be closed.
Correct. Regulatory arbitrage is about finding and taking advantage of loopholes, and shifting business activities to other business units (or even locations) where while those actions are technically legal, they're very, very borderline.
Then you generally couple regulatory arbitrage with money spent on lawyers and lobbying to monitor the existing loopholes, in order to make sure they don't disappear.
What Uber/Lyft are doing is more equivalent to poker: a combination of betting (a large enough war chest to pay lawyers and fines) and bluffing (using marketing campaigns to garner public interest and shame/scare the establishment).
When the stakes get too high (e.g. ride sharing laws in Austin, TX), they fold.