As already mentioned: the tutorial uses an old version of vue.js. It took me some time to figure out why I received a blank page after I added the v-repeat list element. I also didn't look at this discussion here, because then I probably would have saved a lot of time.

I had to change the following:

change <form v-on="submit: send"> to <form v-on:submit.prevent="send">. You can then also remove e.preventDefault() from the send method.
change method ready to mounted as vue.js 2.0 does not support ready anymore.
change <li v-repeat="message: messages"> to <li v-for="message in messages">

If you don't have time to update the tutorial video, maybe you can add a visible note at the top of the page that there had been breaking changes in current vue.js version.

Hello Socket.io