I suspect that you aren't hosting your video on a streaming server, but as a regular file. This means the file has to be downloaded before it can be played, so you also see the download button.

If this is the case, you may be able to add some CSS to hide the download button, but the video will still be downloaded behind the scenes and be available in the browser cache if a user goes looking for it. Look at hosting your video on a dedicated video hosting platform so it can be streamed instead.

I hope this helps.