How can I prevent jittery video playback on High Sierra?
No, Apple did not deliberately slow down your Mac. (As for deliberately slowing down iPhones see this).

The reality is I see this sort of thing all the time, on both Macs and PCs, as well as other devices (e.g. smartphones, tablets, etc).

As time goes by the minimum requirements for software and hardware change, and the configuration of a particular system will have a big impact on how long it will continue to keep up with software changes etc.

Without knowing the full specs of your MacBook Pro (e.g. type of storage device, software, etc), it's nevertheless 8 years of age and obsolete.

As a result, this model will run Mac OS X El Capitan better than it's going to run macOS High Sierra. And, once you're running a particular version of an operating system, this will have much broader ramifications. It's not just the OS, but bundled software such as browsers that have greater requirements. Additionally, some 3rd party software/hardware will no longer work, or they'll have limitations, hence the need to regularly update/replace them as well. 

In general, macOS High Sierra has greater requirements than El Capitan had, and although it still runs on older hardware such as yours, that doesn't mean all features will work on your machine. And while High Sierra can run with 2GB of physical RAM, its requirements are such that it's more RAM hungry than El Capitan was, hence placing a greater burden on your storage device for virtual memory purposes (having a fast SSD is going to handle this better than a traditional hard drive).

In other words, the problem you're experiencing is most likely the result of a scenario something like the following:


macOS High Sierra needs more memory to run (both in terms of RAM and graphics)
It therefore uses more of your physical 8GB RAM, thereby leaving less RAM available for other software etc
In response, macOS High Sierra makes more use of virtual memory to help manage the limited memory resources
This places a much greater burden on your storage drive which is having to deal with a lot more read/write operations
Your video playing software is potentially having to make more use of virtual memory and your storage drive is having to perform even more read/write operations as it has to deliver the video as well as everything else it's doing
End result: A stuttered playback experience.


Summary 

The overall burden on your system from having High Sierra installed (along with all of its associated software etc) is much greater than having El Capitan installed. And, this overall burden will be more obvious with some functions than it will be with others. Unfortunately, playing video files is one such candidate for this. 

If you had a 2011 MBP you might have been able to address this by increasing your RAM to 16GB, but that's not an option here. If you don't have an SSD already, then installing one will definitely help. If playing videos is the main purpose of this machine, then leaving it with El Capitan installed may be an option for you. Otherwise it's time to reconsider your setup as your MBP is no longer able to meet all of your needs.