I only draw a star from (and would add him again) because video does not run over the network "smooth". I hope it is understandable what I mean. The videos are minimal choppy but you can tell it.
I know not whether it is up to the software or the Fire TV stick, because the Raspberry Pi I do not have this feeling. Here, the Fire TV Stick has significantly better hardware and at the Fritz box it should not be, but perhaps because the video for the moment still have to take a detour via the Raspberry Pi.