To recognise what video your player is playing (360 or plain), there are two ways.
1. Direct querying to YouTube API.
You can simply query by this URL:
https://www.googleapis.com/youtube/v3/videos?part=snippet,contentDetails,status&id=<YOUR_VIDEO_ID>&key=<YOUR_API_KEY>&alt=json
To obtain an API key, you must visit this page to check guide if you haven't it yet: https://developers.google.com/youtube/v3/getting-started. In the response, you should read the value contentDetails.projection as defined there: https://developers.google.com/youtube/v3/docs/videos#contentDetails.projection.
2. Indirect guess of video format.
First way is doing additional HTTP call which may beat performance, so we can use this way also. Iframe API Player has .getSphericalProperties(), which will be empty object if there is rectangular (plain) video presented, but will have something like {yaw: 0, pitch: 0, roll: 0, fov: 100.00004285756798}, if you're using 360 video.