Honestly it looks like this IC has only some kind of current limitation ("current control" with a fixed off time), but no real overcurrent/short circuit protection. The overtemperature protection won't help either, as it is most probably too slow to protect the FETs in a short circuit condition. Indeed the datasheet states that the existence of the overtemperature detection "should not imply that output short circuits are permitted"...
A safe H-bridge needs overcurrent sensing on all 4 FETs. With a common current sensing on the lowside, you can only detect overcurrent flowing through the lowsides, i.e. short circuit of the load or a short circuit to power on the outputs. Actually I think that the FETs will be destroyed in these fault conditions, even if the overcurrent sensing should be fast enough (not sure about this), as the bridge is not completely disabled, but just switched off temporarily. That's probably why they call it current regulation, not overcurrent protection.
Furthermore in some ("decay mode") configurations, the bridge seems to enter freewheeling on the lowside after sensing an overcurrent, so the lowside transistors are switched on for a certain time. This is ok if you assume in a normal operation condition (current blocked by the highsides), but with a short circuit to power on one of the output terminals, this could destroy the lowside FETs. And of course a common current sensing on the lowside makes it impossible to detect a short circuit to GND on the outputs, so the highside transistors will be most probably destroyed when shorting the outputs to GND.
BTW: even with OC sensing on all the 4 FETs, the highsides can still be destroyed in a reverse current condition. I.e. the bridge supply voltage is low and the outputs are connected to power, as then the current can flow in reverse direction through the highsides.