Are they auto-paused, i.e., they tried to auto-play and Firefox paused them? You need to click twice on those to start them. Or is the problem after you clicked (twice)?

Otherwise, how about "the usual":

If a site is generally known to work in Firefox, these are standard suggestions to try when it stops working normally:

Double-check content blockers: Firefox's Content Blocking/Tracking Protection feature, and extensions that counter ads and tracking, may break websites that embed third party content (meaning, from a secondary server).

(A) Do you see a shield icon toward the left end of the address bar, near the lock icon? More info on managing the Tracking Protection feature in this article: Enhanced Tracking Protection in Firefox for desktop (before Firefox 70: Content Blocking).

(B) Extensions such as Adblock Plus, Blur, Disconnect, DuckDuckGo Privacy Essentials, Ghostery, NoScript, Privacy Badger, uBlock Origin or uMatrix should provide toolbar buttons to manage blocked content in a page. There may or may not be a number on the icon indicating the number of blocked items; you may need to click the button to see what's going on and test whether you need to make an exception for this site.

Cache and Cookies: When you have a problem with one particular site, a good "first thing to try" is clearing your Firefox cache and deleting your saved cookies for the site.

(1) Clear Firefox's Cache

See: How to clear the Firefox cache

If you have a large hard drive, this might take a few minutes.

(2) Remove the site's cookies (save any pending work first). While viewing a page on the site, click the lock icon at the left end of the address bar. After a moment, a "Clear Cookies and Site Data" button should appear at the bottom. Go ahead and click that.

In the dialog that opens, you will see one or more matches to the current address so you can remove the site's cookies individually without affecting other sites.

Then try reloading the page. Does that help?

Testing in Firefox's Safe Mode: In its Safe Mode, Firefox temporarily deactivates extensions, hardware acceleration, and some other advanced features to help you assess whether these are causing the problem.

If Firefox is not running: Hold down the Shift key when starting Firefox. (On Mac, hold down the option/alt key instead of the Shift key.)

If Firefox is running: You can restart Firefox in Safe Mode using either:

• "3-bar" menu button > "?" Help > Restart with Add-ons Disabled
• (menu bar) Help menu > Restart with Add-ons Disabled

and OK the restart.

Both scenarios: A small dialog should appear. Click "Start in Safe Mode" (not Refresh).

Any improvement?

Ad block turned off. Cache cleared. Started in safe mode. Started with add on disabled. Any other possibles?

Just to confirm the videos are compatible with an uncustomized installation, could you try:

New Profile Test

This takes about 3 minutes, plus the time to test the problem sites.

Inside Firefox, type or paste about:profiles in the address bar and press Enter/Return to load it.

Click the "Create a New Profile" button, then click Next. Assign a name like July2020, ignore the option to relocate the profile folder, and click the Finish button.

After creating the profile, scroll down to it and click the Launch profile in new browser button.

Firefox should open a new window that looks like a brand new, uncustomized installation. (Your existing Firefox window(s) should not be affected.) Please ignore any tabs enticing you to connect to a Sync account or to activate extensions found on your system so we can get a clean test.

Do the videos play in the new profile? Does the Enhanced Tracking Protection shield turn purple?

When you are done with the experiment, you can close the extra window without affecting your regular Firefox profile. (July2020 will remain available for future testing.)

IMPORTANT: Creating a new profile may change your default. If your regular profile has a Set as Default Profile button after this test, click that to make sure your next startup doesn't yield a surprise.