There's code for this merged in https://gerrit.wikimedia.org/r/#/c/312327/ but it needs some work before we can release it.
[x] https://www.mediawiki.org/wiki/Beta_Features/Package work:
[x] Re-word name (current value is "Video.js" which isn't helpful).
[x] Re-word description (current value is "Updated audio/video player with cleaner look and mobile compatibility." which isn't good enough).
[x] Re-do screenshot (current one is https://gerrit.wikimedia.org/r/#/c/312327/39/resources/BetaFeature_TMH_VIDEOJS.svg not in keeping with the rest of the set).
[x] Create a description page for the beta feature on MW.org.
[x] Create a discussion Flow page for the beta feature on MW.org.
[x] Add a compat block for JS (at least).
[x] Enable the BF in Beta Cluster
[ ] Make sure everyone's happy (Product&Design review. Security review. Performance review.)
[ ] Test a fair bit.
[ ] Announce and release.