I managed to get it working, although it requires clumsy workarounds. Here's what worked for me:
1. Purge Slingplayer from your Mac. This is important. I had old stuff that was preventing me from installing the latest plugin, which you need. I ended up doing a system wipe and reinstall (not restore) from ground up. Not just for Slingplayer, for other performance issues too.
2. Go to Slingbox.com > Watch, and follow the instructions to install and configure the latest plugin.
3. This should get you going, IF you've been successful with step #1. If it tells you your browser/computer isn't compatible, you haven't been successful with step #1.
4. Whenever Slingbox hangs in 'loading/intializing' state, you may need to kill the Slingplayer process using Activity Monitor and try again. It will likely then tell you that the plugin isn't installed, but if you refresh the browser window a couple of times it will start working again.
See what I mean about clumsy workarounds? It's garbage software. I'm told it's more stable with Firefox, but I don't want to run multiple browsers and Safari is in my ecosystem.
Good luck.