Oxen welcome to the Seven Forums.
Seeing as you haven't filled in your system specs, would have helped if you hadn't blocked out that info from that dxdiag screen shot. Little things like that can make it much easier to help.
As for the install error, the installer with Steam is probably using the web installer version which can (and most often is) be buggy. Try using this instead, Download details: DirectX End-User Runtimes (June 2010)
download, extract and run the dxsetup found in it.