The website uses SVGs for animation instead of the canvas2d API, I'm fairly certain that's the cause.
(honestly I love SVGs for static images or at most one or two animations when used on a web-page, but if you're not using canvas2d or even webgl with a thin shim for anything more complex than that, mobile users will suffer)
Could it be a memory leak? Or simply too many animations for my ageing phone to handle?