In relation to the timing of those gifs, we should consider that they were taken when Matteney was the most far away of happening in real life: although it had not been announced, at that moment Court was in the beginning of Coco's pregnancy, there was no way, in the horizon, that they could see each other together, maybe that explains their subliminal sadness, the one that has been captured by the camera lens and we still sense, today, watching the scenes.

And the fact that Friends was basically done and they wouldn’t see each other every day any more.

I also think it has a bit to do with their past and what they’ve been through. The things Courteney says about Matthew are definitely related to his addiction troubles and how they were all very worried about him and nearly lost him (I think that bit is also part of the interview). So yes, the timing definitely plays a role and leads to that somber mood…