What is the meaning of the cop's words?

It's just an expression.

What, in the modern times, makes Christmas Christmas? Gifts, trees and fire, hot chocolate... these kinds of things. Same about Easter, that has chocolate eggs, and so on. The cop says it's going to have to be cancelled because nothing of what makes Christmas Christmas is happening, due to the terror Jack is putting Christmas into.

And adding:

In The Nightmare Before Christmas, there are lands of holidays, where for the people inside that land, the holiday in question is work. A "presentation" night of sorts. If they see that way, might as well be that other people do as well, and then, "Christmas was cancelled," because the Christmas beings couldn't do their job.

Of course the Christmas period can't be cancelled but this expression is usually said in times when the situation is dire or awful.

It basically means that the group had been planning on celebrating Christmas but it is going have to be postponed or cancelled because of the situation they are in.

I think it's also referring to the trope "Christmas is Cancelled" in many previous Christmas Specials.

Classic Examples: https://en.wikipedia.org/wiki/Rudolph_the_Red-Nosed_Reindeer_(TV_special)

Christmas Eve comes and while everybody is celebrating, Santa reluctantly announces that the weather has forced him to cancel Christmas, but is soon inspired by Rudolph's red nose. He asks Rudolph to lead the sleigh.

https://en.wikipedia.org/wiki/The_Year_Without_a_Santa_Claus (Santa has a cold, starts taking a vacation, Christmas is cancelled unless someone can make Santa believe he's believed in)

https://en.wikipedia.org/wiki/Santa_Claus_Conquers_the_Martians (The Martians kidnap Santa to try to cancel Christmas -- instead they adopt the holiday, returning Santa to Earth and turning one of their dudes into Santa.)

https://en.wikipedia.org/wiki/How_the_Grinch_Stole_Christmas!_(TV_special)

[The Grinch] finally has enough and decides to stop Christmas Day from coming to Whoville at all"

Santa Claus is viewed in these media as the KEY element of Christmas: https://tvtropes.org/pmwiki/pmwiki.php/Main/SantaClausmas

https://tvtropes.org/pmwiki/pmwiki.php/Main/SavingChristmas

Extra points if, on realizing the predicament, someone remarks, "Christmas is going to be canceled!"