You sure about that? It breaks when you use timecodes, but dealing with those cleanly in phpbb3 is a bit of a sanity killer.
Just remember to use the link from the 'Share' tab underneath a video. This is also mentioned in the tooltip when you hover over the youtube bbcode button on the post creation page.
Webm is basically gif 2.0. You can use http://www.webm.land/ or any other service that allows the direct linking to webm files.
You can also use the attachment system of the forum, but then you're limited to 1MB max and you have to jump through a hoop to get it to play nice with the webm tag. (Get the actual link by opening the preview of your post after uploading the attachment, then right-click on the attachment and copy the link address. You can't use the inline attachment link in the webm tag.)