This does not work like that, because you did not use authentication. More about that see here:
Identifying your application and authorizing requests
Every request your application sends to the Fusion Tables API needs to identify your application to Google. There are two ways to identify your application: using an OAuth 2.0 token (which also authorizes the request) and/or using the application's API key. Here's how to determine which of those options to use:
If the request requires authorization (such as a request for an individual's private data), then the application must provide an OAuth 2.0 token with the request. The application may also provide the API key, but it doesn't have to. If the request doesn't require authorization (such as a request for public data), then the application must provide either the API key or an OAuth 2.0 token, or both—whatever option is most convenient for you.
To access a fusion table with App Inventor, you have 2 possibilities:
- use the built-in fusiontable control blocks, how to set up everything for App Inventor please see the Pizza Party tutorial
- use the web component with authentication, for details see here