They work almost correctly (bug 1194665) in Firefox for Android. In Firefox OS there's a black video element that can't be played.
On my testing devices they don't play in Firefox on Android either, but the failure mode is a bit different: in Firefox OS you get a <video> element without a src attribute, in Firefox on Android a <video> element pointing to an empty.mp4 video. Site uses video.js or a script derived from it (according to the vjs- prefixed classnames in the markup). But many other video.js-based solutions work just fine in Firefox on Android, so either they are using an old version on Wired or there's a problem with some other component. This is tricky to debug because for some weird reason, those videos don't play neither in Chrome on Android nor in the Android stock browser on my test devices - I have no idea why :-/
I can play those videos in Firefox for Android and Chrome on my Nexus 5 (Android 5.1.1).