Lemuel,
Yes the MS Windows Administrator account is conceptually the same as the Root user in Linux/Unix flavors. Of course the underlying file access and process control are handled differently. But it is also the same range of hassles to get a fully active Root user Desktop configured on many of the Linux flavors.
ESRI's "can you run it" applet from Systems Requirements Lab has both an ActiveX and a Java flavor--so your choice of browser used (IE, Chrome or Firefox) and the security mode and run permissions can end up garbled during the applet setup.
If the applet did load but only gave a partial result, you can remove it from the "Programs and Features" panel of the Control Panel--look for "Systems Requirements Lab" and uninstall. Then try downloading and running it again, perhaps a different browser and watch for the security notification to let it complete an analysis.
Which ever way you proceed, the Forum is here to help to get you on track.
Stuart