I disagree with the idea that reduced animation means all slideshows should fail. If the slideshow works with some settings and fails with others, it’s confusing and I would consider it to be unreliable behavior.
It does not mean all slideshows should fail, no. The Jetpack slideshow doesn’t work with that setting active, because the plugin chooses to respect that setting, and if MacOS, Linux, Android or iOS were to introduce similar settings, Jetpack would likely respect it there as well. Other plugins might choose not to respect that setting, but that’s a choice the developers of those plugins have to make.
It’s even worse that the non-functioning play/forward/back buttons are displayed.
Those buttons worked fine for me, both on your site and on another site where I tested this on Win 10 with that setting active. So the buttons not working for you is unrelated to this setting, and likely something else specific to your computer or browser.
Perhaps it would be better if Jetpack allowed the website designer to choose if the animation will work with that setting or not.
As per the reply in the GitHub issue where I reported this, it doesn’t look like that’s going to happen. So if this is a deal-breaker, it looks like you’ll have to use a different slideshow plugin, yes.