Why does she say, "it’s cake," (instead of, "it’s a cake," or, "it’s the cake")? Why does she talk like a foreigner?
There are certain things that could be put in a box, and it would sound odd if I didn't use an article. For example:
Guess what's in this box?
It's puppy! *
It's sewing machine! *
It's vacuum cleaner! *
(The * character denotes an error. These should be "It's a puppy," "It's a sewing machine," "It's a vacuum cleaner.")
However, if there was more than one of something in a box, and the noun was pluralized, no article would be needed:
Guess what's in this carton?
It's sewing machines!
It's vacuum cleaners!
From a grammatical perspective, some nouns can function as mass nouns, meaning that these words can function as a plural, even when written in the singular. Therefore, no article would be needed:
Guess what's in this crate?
One way to tell if a word can function as a mass noun is to try to use some in front of the singular form, where some means "an unspecified amount of". This won't work if the noun can't be used as a mass noun:
What would you like for your birthday?
I'm hoping for some candy.
I'm hoping for some coffee.
I'm hoping for some cake.
I'm hoping for some clock.⁎
"I'm hoping for some clock," would be grammatical if the person means, "I'm hoping for a clock of some kind," but not if the person means, "I'm hoping for some unspecified amount of clock."
Because cake can indeed function as a mass noun, the sentence in the video sounds like one that would be uttered by a competent native speaker. No article is needed (although one could be used – there would be nothing wrong with, "It's a cake!").