I know this thread is about a year old, but for anyone else wondering how to make the "continue watching on mobile" go away then you just need to disable it in the basic settings 
Best posts made by PiggestFan
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Opera GXRE: How to Remove Floating Buttons when watching youtube videos.
Latest posts made by PiggestFan
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Opera GXRE: How to Remove Floating Buttons when watching youtube videos.
I know this thread is about a year old, but for anyone else wondering how to make the "continue watching on mobile" go away then you just need to disable it in the basic settings