The minimum requirements are based on the Express edition you’re attempting to install:
Express for Web (Web sites and HTML5 applications) - Windows 7 SP1 (With IE 10)
Express for Windows (Windows 8 Apps) - Windows 8.1
Express for Windows Desktop (Windows Programs) - Windows 7 SP1 (With IE 10)
Express for Windows Phone (Windows Phone Apps) - Windows 8
It sounds like you’re trying to install the “Express 2013 for Windows” edition, which is for developing Windows 8 “Modern UI” apps, or the Windows Phone edition.
The similarly named version that is compatible with Windows 7 SP1 is “Express 2013 for Windows Desktop”
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