No - the 8.1 SDK is fine. You might want the Windows 10 SDK if you were developing to use new technologies in Win10, but the 8.1 SDK is all you need in general. Also, that's a required separate install only if you will be using the bundled VS Shell.
I had never heard of that library before, but it appears to be specific to VS2015. Is your user building a mixed Fortran-C application? If so, he'll need MSVC installed and not just the VS Shell.
We distribute our libraries for our current software as built with PSXE2017 and VS2013. That works fine for our users who link our libraries with with PSXE2017 but have installed VS2015. The libraries contain references to the iob functions, which MS removed in VS2015, but to keep backwards compatibility put in the legacy_stdio_definitions.lib. So now PSXE2018 comes out and our users are getting that and trying to compile and link using our libraries, but with the VS shell 2015 in PSXE2018 those libraries don't exist. So for the moment we can't have users use the latest compiler. That has never happened to us before. Took me a while to realize that VS2015 shell was being used. Thanks for your help.
This was a problem even with many older versions of IVF and MSVC. So often that I knew from experience what the problem was and what to do whenever I saw linker errors related to symbols with iob and errno in them. These problems have become more noticeable now that MS has made substantial changes to C-STDIO.
Just tried the install on windows 10 with only windows 8.1 SDK installed. We get several screens that say you must install SDK 10.0 for the shell to be installed. Proceeded with the install anyway and VS shell doesn't get installed. We are going back to do it with SDK10.0, But I'm confused as to why you don't think it needs it, and the instructions don't say it is required, but the installer does.
I've never seen the request for the Windows 10 SDK before. I have been away from Intel nine months, though, so I suppose something might have changed. But I have installed the 2018 version without the WIn10 SDK and had no issues.