What you are trying to do definitely works.... but....
your success depends on the TV, the HDMI cable, and the HDMI adaptor you are using from your Macbook.
There are different versions of HDMI and if only one of your components is old or incompatible then nothing will work.
(Search for "wikipedia hdmi version" if you want to know more)
Try another cable - that's the easiest... followed by another HDMI adaptor/dock.
You should be able to see the external display in Settings > Displays.
If that is the case, then you can set the type you need (mirror or another display) and simply use it.
It isn't a browser or software thing - as I do this all the time with Youtube.
And one other thing... make sure the HDMI cable is fully inserted. I have had many customers with slightly damaged or stressed HDMI plugs or sockets that are very fiddly to insert correctly.