yeah, i have that problem with Chrome. for me it was a ram issue, i downloaded advanced system care 8 and it has a easy sweep feature to clear ram with a click, i have it fixed on my screen and click it every 10 or so pages and problem solved
From what I understand, once the gif loads the first time, it's up to their browser to display it properly, their operating system to run the browser properly, and their machine to run the operating system properly.
So, pretty much, if they can reach the end of the gif but it's not smooth, then it's not their internet connection.
TL;DR - it'll usually be a problem somewhere between the website and the browser, or a matter of processing power. Internet only affects how long it takes to load the gif, not play it.
i wish i had the money that the unicyclists have. enough to not have to work and do everything until im bored enough to ride a unicycle. the difference is with me, i dont think i'd ever get that bored and would always have fun in good ways