UPDATE: I tried, as an experiment, plugging in an old (wired) Apple Mouse - not a Magic Mouse - and everything worked perfectly. So the problem is presumably lying somewhere in the mouse drivers? It's good that I've solved the problem, but it would be nice to know why this has happened.
UPDATE 2: Entire problem was fixed by purchasing a Logitech G602 and using that. Not my favourite mouse, but it works perfectly on everything. So it must have been a mouse driver issue.
New problem I'm having. Can start EG Launcher no problem. Once I'm in, pressing 'Launch' takes several clicks before it responds. Game goes through the loading screens OK, but when I come to select 'Battle Royale' again it requires several clicks. Once I'm in the lobby, buttons do not respond to clicks at all. Can't even quit the game through normal methods, I have to do Cmd-Q.
A similar problem is affecting me when I try to run the game through GeForce Now. Normally my MacOS pointer arrow will disappear from the screen once the EG Launcher screen appears, and will be replaced with a Windows-style pointer. For the past few days, however, my Mac pointer remains on screen and the Windows pointer doesn't appear at all. So the game doesn't respond no matter where I click.
My assumption was that my Mac is not communicating properly with whichever server it's trying to connect to, perhaps because of an internet connection issue, or because of the update to Mojave. However, I don't have any problem running Overwatch through GeForce Now. Furthermore, I can run Fortnite BR just fine on my iPhone (over the same internet connection).
Can anyone think what might be causing this, and what I might be able to do to resolve it? I'm using a 2014 27" 5K Retina iMac, with 32GB RAM and a Radeon R9 card with 4GB VRAM.
By the way, my mouse works perfectly the rest of the time in all other functions (except Steam, where I've been having a similar issue for months... I'm seeing a pattern here...).
[EDIT: Small update - everything worked fine yesterday evening, now today I've got problems again. Wondering if my internet connection - a 'mere' 40MBps - is to blame? I can play the game, but my mouse is unresponsive unless I hold down the RMB. ??? What I can't fathom is that no one else seems to be having this problem - although to be honest I don't know what to search for to find out who is.]