You are correct; the Slingbox SOLO does not work with the Chromecast. The softwares are not compatible with one another at all. Think of it like trying to put a game that required Windows 98 on a Windows 8 computer; if you are lucky it might let you install the program, but it won't run. I have placed an article below that goes over the compatibility of each unit versus the different connected devices:
The Roku works in an almost identical manner to the Chromecast though, and is compatible with the Slingbox SOLO.
I hope this helps!