Yes, he's talking about queuing up as a solo player in "Quick Play" there, which is akin to non-ranked for League of Legends, except unlike League of Legends, if someone leaves a match another searching player can be matched and filled into the team (back fill) so teams aren't uneven for the rest of the match. Unfortunately this means sometimes you get thrown into a game 10 seconds before a loss, which feels kinda shitty, but doesn't actually give you a loss on your record.
Ranked/Competitive has not been released yet so there's no way he could've queued up for it yet.
In beta, there was no "back fill" option in ranked queue, so that could never happen. The slots were reserved for the people who started the match and they could reconnect if they got disconnected (just like League). Penalties for leaving ranked queue were also much harsher.
edit: Now that I watch the video more I am realizing it was pretty misleading the way he compared Overwatch's "Quick Play" to League's "Ranked Play" without actually calling that out. He DID make it sound like you could lose a competitive match by joining a game 10 seconds before end by doing a comparison like that. But I mean, the guy is paid by Riot... so why would I expect him to be unbiased and/or bring up all the facts like solo rating means jack shit anymore? /shrug.