Hold person paralyses the NPC, so they fall
According to the situation is:
An NPC spell caster that is using spider climb
This indicates that the NPC has cast the spider climb spell on themselves.
However, the NPC automatically loses concentration on spider climb if paralyzed by hold person due to being incapacitated (Basic Rules, p. 97):
The target must succeed on a Wisdom saving throw or be paralyzed for
The description of the Paralyzed condition says (Conditions, Appendix A):
- A paralyzed creature is incapacitated (see the condition) and can’t move or speak.
That by itself breaks concentration (Basic Rules, p. 84):
You lose concentration on a spell if you are incapacitated or if you die.
Failing the saving throw against the hold person spell causes the NPC to fall unless something else is keeping them up there.
There is no Dexterity check involved
The issue at hand is the NPC's concentration on the spider climb spell ending. If they successfully save against hold person, the PCs may still knock them down with the arrows' damage.
Spider climb has a duration of "Concentration, up to 1 hour", and its description states:
Until the spell ends, one willing creature you touch gains the ability to move up, down, and across vertical surfaces and upside down along ceilings, while leaving its hands free. The target also gains a climbing speed equal to its walking speed.
If the PCs hit the NPC after a successful save against hold person, the damage will induce a Constitution saving throw to maintain concentration (Basic Rules, p. 84):
Whenever you take damage while you are concentrating on a spell, you must make a Constitution saving throw to maintain your concentration. The DC equals 10 or half the damage you take, whichever number is higher. If you take damage from multiple sources, such as an arrow and a dragon’s breath, you make a separate saving throw for each source of damage.
If the NPC fails that saving throw, then the NPC will fall. If they pass, they'll stay up there.
Two arrows hitting is better than one.