Your embed code will work as long as all your users are using HTML5 compatible browsers. If some users are using computers with older operating systems and/or web browsers, you may want to include some Flash embed code as a fall-back.
The part that catches my attention is:
Are you serving the videos from Moodle or are they hosted on another service/website?
The reason I ask is because serving large video files from Moodle puts a heavy load on your Moodle installation and your server may not have sufficient power to serve the videos to several users at a time. If you have access to several computers, tablets, and phones, and a fast commercial-grade internet connection (e.g. a computer lab), you can test how well the server handles it by playing back videos from Moodle on all of them at once. Start with 5 videos (you can playback more than one video from each computer/device) and gradually increase the number until your Moodle becomes unresponsive and/or drops connections.
If the number of concurrent videos you can play back from Moodle is insufficient (remember that not all your learners will be watching at the same time) then it's time to consider either "beefing up" your servers (increasing memory limits and timeout times, installing more of servers, switching to more powerful ones, or switching to cloud hosting), or hosting the videos on a dedicated video hosting platform or service.
I hope this helps