The Moa might have survived if the Maori had tried and succeeded in domesticating them.
The moa were, in all probability, undomesticable. The early Maori were familiar with domesticated birds (chickens etc), and indeed had domesticated animals (dogs at least). But they didn't domesticate the moa.
While it's impossible to be sure, we do know that the moa took
ten years to reach breeding age. That's all species of moa; the bigger ones grew faster, but didn't take any longer to reach breeding age.
Ten years is a heck of a long time to go about trying to domesticate an animal. The effort required to feed them for that long (meat etc) isn't really worth the reward, even
if they could be domesticated at all. Offhand, I can't think of
any domesticated animal which takes anywhere near that long to reach breeding age, for good reason.
On a broader note, there are indeed a variety of species which survived by flukes in OTL and might have gone extinct, or who were pushed into extinction by contingent factors in OTL and which might have survived in OTL.
Some have already been mentioned: American bison, passenger pigeons, etc. Maybe Carolina parakeets, too. In Australia (well, Tasmania, really), the Tassie tiger (thylacine) appears to have been swept into extinction by a combination of human hunting
and an introduced epidemic disease (probably a variant of canine distemper). If those factors hit at different times, then the Tassie tiger may still be around. (As I had happening in DoD).
New Zealand also has a variety of bird and other species which survived only on isolated offshore islands, and thus may well have gone extinct in an ATL if rats or cats or so forth made it to those islands. Or ones which went extinct if cats or rats weren't introduced: the Stephens Island wren, for instance, which was wiped out when cats were introduced into its last refuge (although it was more than one cat, urban legends notwithstanding).