Same for me, it won't happen anything. No matter what movie I try to play. On the console I get this error:

./ubuntu12_64/html5app_steam.sh: line 4: 28027 Segmentation fault      (core dumped) ${DIR}/html5app_steam "$@"

This is the content of that file:

#!/bin/bash
DIR=`dirname $0`
export LD_LIBRARY_PATH="${LD_LIBRARY_PATH}:.:${DIR}:${DIR}/../linux64:"
${DIR}/html5app_steam "$@"

Add me to the list of not being able to play videos, I'm getting the exact same error message as NoXPhasma.
https://gist.github.com/lucifertdark/584c14275612e8e3c4a8070d428d8a02

It seems like it's missing configuration

GameAction [AppID 1059340, ActionID 1] : LaunchApp changed task to UnlockingH264 with ""
GameAction [AppID 1059340, ActionID 1] : LaunchApp changed task to WaitingOnWideVineUpdate with ""
Opted-in Controller Mask for AppId 1059340: f
Game update: AppID 1059340 "", ProcID 10516, IP 0.0.0.0:0
GameAction [AppID 1059340, ActionID 1] : LaunchApp changed task to Completed with ""
Starting app 1059340
>>> Adding process 10516 for game ID 1059340
CAPIJobRequestUserStats - Server response failed 2
>>> Adding process 10517 for game ID 1059340
>>> Adding process 10518 for game ID 1059340
>>> Adding process 10519 for game ID 1059340
>>> Adding process 10520 for game ID 1059340
Game removed: AppID 1059340 "", ProcID 10516 
Exiting app 1059340

Me too, same issue, on Kubuntu 18.04 despite having watched videos on Steam successfully in the past. Only just noticed the issue today, or I'd have come here looking for this issue sooner.

Same here, I have tried playing videos on Kubuntu 18.04, 19.04 and 19.10, but it just closes and noting plays. It was working fine before the library update.

Same issues on Linux Mint 19.2 and 19.3 I hope this will be fixed soon

I too suffer from this problem on the latest KDE Neon (Ubuntu 18.04 derived).
Tried it on 2 different hardware setups. (Intel integrated graphics and a non-integrated AMD card)

Same on OpenSuSE Leap 15.1 with plasma.

Same here on Arch Linux with the Steam Runtime enabled. All videos from the Steam Library (Steam store videos work fine) fail to play. When pressing play, the pop up appears and then disappears. When running Steam from the terminal, a segmentation fault in the HTML5 Steam app occurs:

./ubuntu12_64/html5app_steam.sh: line 4: 12311 Segmentation fault (core dumped) ${DIR}/html5app_steam "$@"

Other users have reported this issue on the Steam for Linux forum:

https://steamcommunity.com/app/221410/discussions/2/1638675549001453606/

Library videos are now playable again. Ubuntu 19.10 nvidia 440.59 drivers.

Confirmed working again on Ubuntu 18.04.4 as well. EDIT: Steam beta 2020-02-13.

Confirmed working on Mint 19.3 but only if you have the Beta channel for steam!

I confirm the beta channel did the trick.

Using Kwin scripts to auto-tile windows, i noticed the window when not in fullscreen, doesn't detect changed window dimensions (not using standard ratio), the canvas doesn't resize.

Ah I forgot I'm always using the beta channel.

I can also confirm that it's working in the Steam Beta client (built Feb 15 2020). Still not working in the non-beta client (built Feb 11 2020).

Confirm that the library videos are playing on OpenSuSE Leap 15.1 with NVIDIA 440.44 in Beta.
Thanks for fixing this, looking forward to having it pushed into the regular release.

I can confirm the issues with the resizing mentioned by Bumbadawg:

When I switch to full screen, the frame and content adapt correctly. When I go back to windowed mode, the image does not resize again but is simply cropped left and bottom.

FWIW, using a bog-standard Ubuntu [18.04.4] desktop, resizing is fine as well.

Full screen & maximized window give the full picture, but resizing to a smaller window cuts off half the picture for me too, Ubuntu 19.10 desktop (Gnome), the videos play properly in Big Picture mode but it switches back to the standard desktop when exiting the videos.