Triac drivers with or without zero-crossing detection
The description states that the triac switches off automatically at zero crossing and when there is no gate pulse. Does this mean this a zero-crossing detecting triac driver?


No. Triacs have the characteristic that, once triggered, they stay on until the current through them falls to zero (or very close). This makes them very easy to use in AC circuits because the voltage (and current)falls to zero every half-cycle. It also makes them almost useless in DC circuits - unless you want something to latch on until power is switched off.

The term "zero-cross triac driver" refers to when the triac is turned on.

See my answer to Confusion with TRIAC firing and zero crossing point for more details and some graphics on this subject and when to use zero-cross and not.