@Ivan G. As of right now, the default browser for Synthetics is google Chrome. There is currently no feature that will allow you to launch synthetics via IE. Maybe on the roadmap for a future release. I would recommend putting in a Request Feature Enhancement (RFE)
You can create a RFE from the following Link: https://answers.dynatrace.com/content/idea/post.html
Please note, it is important to select the location as "Product Ideas" as this is where the PM's go to select features for their roadmap.
You do not need the plugin on the server. If you want to record synthetic click paths the plugin is required on your Company laptop/Desktop that is used to work within the Dynatrace UI.
what version is the video player? it might be an outdated platform. I would suggest opening a support ticket with Dynatrace. Are you able to view the video in a chrome browser on your desktop? I would assume that if you can see it via chrome, that the synthetic monitor should as well.
@Ivan G. I'm going to say that the technology that is serving up your video is either outdated and/or unsupported. My reasoning is that I am able to hit youtube videos with my synthetic monitor with no issues, as well as interact with the page. I would recommend opening a support ticket where a Dynatrace Support rep can dive deeper into this issue.