The idea would be to open an embedded video in an external video player. (For Windows: VLC, MPC-HC, MPC-BE, PotPlayer, Windows Media Player; for Linux: VLC,
mpv, SMPlayer; on Mac: VLC). A good way to do that is to use Firefox addons. (there were also some Chrome addons, but now Chrome seems to go in different direction by removing NPAPI plugins):
Made to send videos to external download managers: can be set to send the video to an external video player. After installing and adding the players as described in this answer, make it easily accessible like so: open the 'customize' options for Firefox and drag&drop the needed icon in a visible location on the toolbar (that will then be visible only during media play).
Start the video and that icon will become visible.
Do not left-click that! (For some sites like youtube multiple streams are available for a title and left-clicking starts them all, as FlashGot is intended for downloading and this is a 'download them all' feature.)
Right click on that and select 'Flashgot options' if you want to select between multiple video players if the case:
Right-click the icon to select the stream to play (different are available on Youtube).
Cross-platform, different video players, different (HTML5 and Flash) websites.
Made to open links in other internet browsers: can open a link into a video player.
Cross-platform, multiple video players, tested in Youtube (other sites may work, although none that I tested does).
Watch with MPV
Made to start internet video in mpv video player. Adds a toolbar icon and a context menu entry and can use a short-key to start. It is supposed to be set to work with other players too (but trying VLC it doesn't seem to work well).
Cross-platform, mpv-based but can be set for other video players, different (but not many) websites
VLC Youtube shortcut
Adds a context menu entry to start playing a Youtube video in VLC.
Cross-platform. Youtube-only, VLC-only.
Cross-platform, Youtube-only, different video players (but only one can be set at the same time; in FlashGot and OpenWith you can add and select between different players).
Last two addons were suggested by a comment made by user3791372. Other addons in the link included in the comment are outdated and even buggy.