How do the buttons look? Are they grayed-out or white?
The first time I opened the load screen, the buttons were grayed-out: all of them. But it was expected, because the browser cache was empty.
I have started a new game, created the character, then opened the load screen and everything worked as expected. I have tested the local version both on Firefox and Chrome. I am on Linux, Sandboxie plus is not available on my system unfortunately, and I cannot reproduce the bug.
Did you reload the game by pressing CTRL+F5? Sometimes it helps. If not, maybe more skilled users have a better idea, sorry.