I think there are two ways you can address this issue for Safari.
The first is using JavaScript to kickstart your animation.
Using Charles proxy, I manipulated the response so that this:
<p class="marquee" id="countries">
became this:
<p class="marquee-pre" id="countries">
Then, I injected the following JS at the bottom of the page:
<script>
$('.marquee-pre').attr('class', 'marquee');
</script>
which immediately addressed the issue.
If you don't mind adding JS to your page, I would recommend this approach.
If you can't add JS, or prefer not to, I found making the following change to the CSS animation also worked:
.marquee span {
-webkit-animation: moveSlideshow 165s linear infinite;
}
to:
.marquee span {
-webkit-animation: moveSlideshow 165s steps(10000) infinite;
}
While this works, I found it wasn't as "smooth" as using linear timing...