How can I download eMindMaps on an Android tablet without having to deal with .exe files?
You can't download and install the application on Android because there is no version released for Android operating system. However, there are alternative applications from the same category. For example, MindMeister. It's works on the same principle as eMindMaps and it's available for installation for Android phones.
Application's page at Google Play: https://play.google.com/store/apps/details?id=com.meisterlabs.mindmeister