We are probably going to here this argument in a myriad of ways in the coming months. The way it is made in the Vox video is probably the least convincing way of making this argument. It's pure speculation, built on zero evidence.
There's little strategic thinking about the interests and the options that the different players have in that video, so you may not spend your time watching it.
It's not for this post, but I don't believe that Brexit will make the EU stronger. It'll be messy. If it doesn't make the EU weaker, this is probably the best outcome we can hope for.