The background is that the spatial library consists of a managed part and a native part. Roughly, the core geometry library resides in the native code, and everything else is in the managed layer. The native code requires the C++ runtime libraries. This is installed with SQL Server, so everything works fine if you install SQL.
The redistributable version we ship as part of the feature pack should redistribute the runtime as well, but it doesn’t. That’s the bug. So, if you install the library on a machine without the runtime, then it will fail.
The workaround is simple: install the runtime manually. Annoying, but effective. You’ll also be fine if you install another package—like the SQL Native Client—that includes the runtime, but unless you also want that component, I’d stick with the stand-alone install.
SP1 for SQL Server 2008 is coming up, but unfortunately, we’ve missed the cutoff to get this in. We’ll try to get this into the next service pack, but that will take some time. In the meantime, you’ll have to use this workaround. I’ll try to get an official KB article published on this as well.
So, apologies for the inconvenience. And thanks to Jason for raising the issue.