For testing purposes I run Edge via the Azure RemoteApp. How can I check which Edge version (Engine, HTML) is run?
Get Edge version when run via Azure RemoteApp
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I work on Edge at Microsoft. Shashed is correct. The answer is "it is not Edge". It is IE 11, with a switched out rendering engine (the old trident engine for the new Edge engine).
If you want to know which version of the Edge engine is being run, its as simple as checking the user agent string. As of today (02/24/2016), it is
Mozilla/5.0 (Windows NT 10.0; WOW64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/42.0.2311.135 Safari/537.36 Edge/12.10514
Note the Edge/12.10514
, that means it is Edge v12. The current shipping version on Windows 10 is Edge 13 (note there has been some confusion on Edge's versions previously).

You can simply open the F12 Developer Tools, go to console and type navigator.userAgent
to get the UA string. See the screenshot:
As the other guys already mentioned you could also download a free VM to test with a more current version of MS Edge.
According to the official page:
Source: https://dev.windows.com/en-us/microsoft-edge/tools/remote/
In case this information is outdated, I've also reached out to the Edge team via Twitter, so keep an eye on this tweet: