Is it possible to create my own users database for a google app engine app, so that it's not required for someone to have a google/openId account when he registers ?
Yes, but you will need to write all utility methods for providing proper authentication for your users. Rather than do this, I would recommending looking into the authentication services that Firebase can provide (Google acquired Firebase in 2014). At the moment, it seems Firebase will become integrated into many Google Cloud Services.