I tried the game multiple times in the browser, and everything worked fine for me, but it's possible that the game didn't had enough time to load properly, which can cause a crash.
Had what I believe to be the same thing happen a few times in the downloaded version as well, during a Challenge almost-always when doing Hold Hands. Rolling back resolved the issue when it occurred, although it would sometimes pop up again. Whatever the dang thing is it is either on my end, or at least isn't game-breaking or causing a complete crash.
I'll see if I can manipulate the circumstances (spamming click while we fight, etc) to see if I can narrow down the cause, but sadly that will have to wait until after I move apartments.