No idea why they call it side load, but it's a way off getting apps on to the Fire TV/Stick which a not available the normal way.
Just tried it and it doesn't work, Youtube opens perfectly in the background but overlaid with a message that it won't work without Google Play Services.
Having done some reading, it seems that it is Google blocking it, rather than Amazon, side loading only allows apps to be loaded which are not available the normal way, so won't work in this case.