Google seems to be experimenting with a brand new layout for the share button within the YouTube Android app, and whether or not this is a change that everyone is seeing, it's one that will probably get some mixed opinions, similar to just about anything else that gets tweaked or changed after a fairly long period of time. For a while the share button in the YouTube app has always sat in the top right corner of the video stream, but it only appears after having touched the display when tapping on the video which also brings up the button to pause the video, the button to expand it and add it to favorites, as well as the videos progress bar.
With this new layout, Google hasn't gotten rid of the old placement of the share button, but they have added it into a new location, sitting quite snugly next to the thumbs up and thumbs down buttons for liking and disliking videos. Without trying to inject too much of a personal opinion about this tiny little change, it feels like this is a much more reasonable spot to put it so you don't have to tap the video and bring up all those overlayed icons to share it. Then again if you're going to be sharing a video from YouTube while it's playing, you're just going to be taken out of it to finish the share process anyways so it almost becomes a non-issue.
This certainly isn't a huge change, and one which many people may not even take notice of. It does however, prompt a question of whether Google will be starting to experiment with reorganizing other parts of the app's video player. Perhaps Google just wanted to see if it was used more by placing it in a new location, or maybe they just personally decided they like it better being next to the like and dislike buttons. Maybe Google will be doing more than just a couple tweaks and they'll give the video player a bigger redesign similar to the new web player. Whatever the case may be, you should be able to see the new share button within the app as of now.