It depends upon your browser, if you can click on the video itself or click on the browser's menu to share, and on having an APP that will load your browser's 'share menu' (as part of it's install routine) with the open command.
I have a few video players on my phone but most don't automatically fixup the 'share menu', and I've not felt the need to dig around and add the feature manually.
Using the YouTube APP or the Firefox browser I can click to share and because I have installed TubeMate (to download or play) and BS Player (stream, or play downloaded video) I can share to them and watch the video that way.
Firefox is usually capable of playing the videos 'well enough' (my phone is a few years old) and TubeMate usually can download from anywhere (and is updated frequently). There was only a week when Vimeo made some changes that TubeMate was finicky, other than that everything has worked flawlessly for years.