The ISS isn't capable of being ran unmanned for any significant length of time. Yes they could escape in an emergency, but they're not going to be leaving "normally" until their replacements can arrive. And that won't be for a while, because as Chris explains in the video, there are no other launch vehicles ready to go beside the Soyuz, and it might be a while before the defect is identified and fixed.

They can't outstay the orbital lifespan of the capsule currently docked. They'll be leaving when it's time to leave (unless a new (empty) Soyuz is launched to replace it (something that has happened once before)).

Yeah, from what I understand, the options are basically to either get a new return vehicle up there before December, or abandoning the station.

It's a bad situation to be in. The end of ISS is certainly an option. I don't think they'll ever let astronauts stay there with an expired return vehicle.

They might be willing to stretch it a little (but probably not much). The limiting factor is decomposition of the hydrogen peroxide used as propellant for the descent module. They can technically get down without it, but it would be a rougher (and riskier) ride.

I wouldn't be excited to return to Earth in that particular Soyuz

It's the only one there. The current crew will be using it to return to earth at some point. The manufacturing defect is in a portion of the spacecraft that is jettisoned before reentry anyway.

The hole is drilled in the orbital compartment of the Soyuz, not in the landing capsule. If you don't forget your spacesuit - which you shouldn't forget anyway - you're reasonably safe.

"reasonably safe"

To be reasonably safe in space is a rather good measure... I do see your point though.

Yeah, he even goes on to say that later....