I did a bit of messing around and I found that:
I can't drag anything when I'm on my primarily, smaller laptop monitor. I can drag things when I'm on my secondary, bigger external monitor.
I believe that my smaller monitor just isn't responding to any mouse movements on the right panel of the game, but it does progress the dialogue and can hover over the 3 buttons on the left.
Both monitors are 1920x1080.
Dunno what the issue is, but hopefully you can figure it out. It's probably an edge case for now so don't stress out too much about it, and if anyone else has that problem, see if they have a dual monitor setup. Good luck!