It's being discussed in the 0.9.7 Release thread.
The short answer is: while Sigil itself is perfectly compatible with all versions of Windows 7, the 2015 VC++ runtime (on which Sigil depends) that's being distributed with Sigil requires Windows 7 to have Service Pack 1 installed.
You can uninstall Microsoft Visual C++ 2015 Redistributable (x64) - 14.0.24210 from Add/Remove Programs (if it appears there) and download and install a version of the 2015 VC++ runtime from Microsoft that works without SP1 (if one even exists--I'm beginning to suspect not) and see if that fixes the problem. Or ...
Make sure both Sigil and the Microsoft Visual C++ 2015 Redistributable (x64) - 14.0.24210 are uninstalled, install SP1 for Windows 7 and try the standard Sigil installer again.
My apologies for this. I had no idea the 2015 VC++ Runtime required SP1 (nor predicted that there would be very many people who did not have SP1 already installed).
I really despise Microsoft sometimes.