Hey everybody, I might have a solution.
In Opera, go to opera://gpu (or chrome://gpu). You will likely see that video encode and decode are done by software, not hardware accelerated. Probably some other things as well.
Go to opera://flags (or chrome://flags), and enable the option, "Override software rendering list". Close and re-open Opera. You will see that videos are now hardware-accelerated.
More info: http://www.webupd8.org/2014/01/enable-hardware-acceleration-in-chrome.html
While you're at it, you could also go ahead and enable hardware acceleration in Firefox. Google "Ubuntu Firefox enable hardware acceleration", it's one of the first results.
I don't know for sure whether this really fixes our problem. It did solve stuttering issues for me, which I continued to experience on my desktop PC on 17.10 after uninstalling Opera, and then again after switching to Mint 18.3. After my switch to Mint, I also had stuttering in ZSNES, which went away after I did the following:
Open NVidia settings
In "OpenGL Settings", disable "Allow Flipping" and move "Image Settings" slider to the right until it says "Performance".
You could also try disabling VSync (also in OpenGL Settings). If you get no screen tearing afterwards, leave it off.
In "PowerMizer", set "Preferred Mode" to "Prefer Maximum Performance".
The "PowerMizer" setting is automatically reset after reboot. To make it permanent, open the "Startup Applications" app and add the following as a new startup application:
nvidia-settings -a '[gpu:0]/GPUPowerMizerMode=1'
Name and describe as you see fit. More info: https://devtalk.nvidia.com/default/topic/832288/how-to-automatically-set-powermizer-to-prefer-maximum-performace-with-340-and-346-drivers/?offset=3
Since I'm no longer on 17.10 on my desktop and I still use my laptop for daily work, I can't tell for sure whether any of the above fixes our problem. It would be awesome if one of you guys could report back.