If I have Vilemaw on the battlefield and my opponent attacks me with a unit that has 8 might, do they deal damage to me or not?

Yes, the attacking unit will deal damage to you, provided its Might is equal to or greater than Vilemaw's Might.

According to Vilemaw's ability: "Enemy units here with less Might than me don't deal combat damage."

• If the attacking unit has 8 or more Might, it is not "less than" Vilemaw's 8 Might, so it will deal its combat damage to you.
• If the attacking unit has less than 8 Might, it will not deal combat damage to you due to Vilemaw's effect.

Note that this interaction specifically checks the units' current Might at the time combat damage is resolved.