What qualifies an Android phone to show up in Android Marketplace filter

You can take a look at Filters on Google Play | Android Developers.

It says:
The results are filtered based on which applications are compatible with that device. For example, if an application requires a camera (as specified in the application manifest file), then Google Play will not show the app on any device that does not have a camera.

Declarations in the manifest file that are compared to the device's configuration is not the only part of how applications are filtered. Filtering might also occur due to the user's country and carrier, the presence or absence of a SIM card, and other factors.

In summary, when determining whether to display your app, Google Play checks the device's hardware and software configuration, as well as it's carrier, location, and other characteristics. It then compares those against the restrictions and dependencies expressed by the application's manifest file and publishing details. If the application is compatible with the device according to the filter rules, Google Play displays the application to the user. Otherwise, Google Play hides your application from search results and category browsing, even if a user specifically requests the app by clicking a deep link that points directly to the app's ID within Google Play.

Hope this helps.