It's not a standard usage, but a whimsical invention. The speaker is using "gull," a noun, as if it were a verb* to describe the gulls' activity. This is sort of an instance of "verbing," like whimsical patterns like "I can't adult today" or "I won a Nobel prize for sciencing harder than the other sciencers." The intended meaning could be understood as "the seagulls are doing their thing."
It reminds me of this quasi-nonsense poem from The House at Pooh Corner:
NOISE, BY POOH
Oh, the butterflies are flying,
Now the winter days are dying,
And the primroses are trying
To be seen.
And the turtle-doves are cooing,
And the woods are up and doing,
For the violets are blue-ing
In the green.
Oh, the honey-bees are gumming
On their little wings, and humming
That the summer, which is coming,
Will be fun.
And the cows are almost cooing,
And the turtle-doves are mooing,
Which is why a Pooh is poohing
In the sun.
For the spring is really springing;
You can see a skylark singing,
And the blue-bells, which are ringing,
Can be heard.
And the cuckoo isn't cooing,
But he's cucking and he's ooing,
And a Pooh is simply poohing
Like a bird.
Pooh "verbs" his own name, "poohing," as the best way of expressing his feelings and describing his own activity of whimsical rhyming. (He also "verbs" an adjective in "the violets are blue-ing," and although "springing" is a real verb, he uses it more in the same way as "poohing," i.e. "spring is doing what spring does.")
This usage in the video, "seagulls are gulling," is paired with "away," used not in a prepositional sense that would mean "getting farther from me," but in a usage that pairs with a verb to mean "doing that verb right away, or enthusiastically, or uninterruptedly." E.g. "I gave the kid a crayon and he's just been drawing away for hours." See meaning 6 here.
* There is also a standard verb meaning for "gull," if a bit archaic, meaning to trick someone.