Not sure about this, but I suspect this has to do with you website running under the
NETWORK SERVICE user. Whatever privileges your website-user has, the same are probably granted / passed on as you try to run your executable.
Is this server on an internal network or protected in some other way? (I should hope so!). If so, you might try changing App Pool that the website is running under to an admin account (in IIS, right click the App Pool running the site, select Advanced Settings, and look for the Identity setting). If I'm right, that will allow you to run your executable as an admin too.
Be aware however, that this may increase the security risk of your setup: Allowing your site to run under an admin account means easier access to your entire server if anyone is able to penetrate whatever security measures you have in place. Make sure access to this server is tightly limited, and preferably, that it in turn does not have access to other systems, since that would in turn make them vulnerable by extension.