Whenever I click on a video link, it automatically takes me to the HTML5 player and doesn't even prompt me as to which player I want to use. Is there a way to force a prompt by altering the application files or something?
I'm stuck with the same issue.
A workaround is to use another browser: I tried Firefox, Dolphin & Opera so far.
All of them use embedded video playback.
Only "Opera Mini" asks for external playback app. See download link below: https://play.google.com/store/apps/details?id=com.opera.mini.native
Try Clearing the Defaults for the app.
Since I don't know what version of Android you're running, I'll explain generally.
Head to Settings -> Apps
Click on the Google Chrome App, then scroll until you see "Reset Defaults"
Now it should prompt you again what type of media player you want to use when opening videos.
If that didn't work, you can try to reset the app to factory defaults. To do that just Clear Cache, Clear Data, Force Stop, then Disable the app. Restart your phone and re-enable the app.
You could also, of course, try disabling Chrome and using a different browser (such as Firefox, Dolphin).