EMILY: I scaled back a lot. I cut two appetizers, I canceled the champagne fountain, and I reduced the catering staff to six servers, not counting the pointman.
Technically a pointman is the head of a military patrol, or in the US, the word is used to mean the person who is at the forefront of a particular endeavour. I think Emily just means the pointman is the person who is coordinating the party and giving the servers instructions, solving any little problem that might come up.
The Annotated Gilmore Girls 