Can `crescent strike` deal the 1 damage to units at a battlefield with a `alpha wildclaw` friendly unit that has more might than all those units?

Yes, Crescent Strike can deal damage to the other enemy units at the battlefield, even if you control an Alpha Wildclaw there.

Here is the breakdown:

1. Alpha Wildclaw's Ability: The Alpha Wildclaw has a passive ability that states: "Your units here with less Might than me can't be chosen by enemy spells and abilities."
2. Crescent Strike Targeting: According to RiftJudge FAQ #9516, Crescent Strike only targets the specific enemy unit you choose at the start of the spell. The "other enemy units" at that battlefield are not targets; they are selected by the spell’s effect based on their location.
3. Interaction: Since the other units are not being "chosen" (targeted) by the spell, the protection granted by Alpha Wildclaw does not apply to them. Furthermore, even if they were being targeted, Alpha Wildclaw's ability only protects your units ("Your units here..."), not enemy units.

Therefore, Crescent Strike will deal 4 damage to your chosen target and 1 damage to every other enemy unit at that battlefield regardless of the presence of your Alpha Wildclaw.