I didn't look at the video but is it the upper pin near the trigger? Technically that pin isn't necessary except for reinforement of the locking block but it's unusual that it would come loose like that in a new gun. I removed both pins from my six month old 23Gen4 and it took a little effort which I'd expect that to be the norm of any new Glock. My older (1997) G22 pins are a little looser but don't walk out.
Anyway it would be disappointing in a new gun but not a deal breaker especially in a state like CA where anything is a hassle. Glock must have lots of experience with issues like this so I'd call customer support and see what they say. You'd think with all the worn frames out there that they have oversize pins. This can't be a difficult thing to fix so I wouldn't send the gun back to the factory if there is no other issue.
One thought, is there any chance someone bubba'd this gun somehow? I know it's new so just bring this up in case something weird happened, that would be a reason to send it back to Glock.
The biggest issue with assembling an AR isn't so much getting the parts together right - it's getting the right parts together.
US Army 1966-69, VFW Life Member, Retired Geek