A lot of people do use gmail but a a lot don't. I thought the total of hotmail/live.com/outlook.com was still larger than gmail. Yahoo still has a whole lot too. But most early adopters of an app like Mailbox probably do have gmail.
I have a personal gmail account but an Exchange account for work. I did get into Mailbox late yesterday but I'm not sure if its worth it to me because my personal mail is rarely time sensitive. So the "email into a to-do list" aspect of Mailbox doesn't help me much. Mailbox also wanted me to enable my "All Mail" folder in gmail which I don't like and turned off since I didn't see the need to have messages in multiple places (both All Mail and the folder I filed it in).
But the design is beautiful. Just not sure if it works for me yet.
Yeah, the combined number of Outlook, Hotmail, and Yahoo address is higher than Gmail. But most that use those either have them for work or aren't they type that looks for new technology in an app like mailbox.
Gmail users are the current target audience because they are typically younger and more cutting edge. It's also easier on their servers to pick a single service to start with. Gmail would provide the the largest exposure right away.
They have said that full support for other platforms is coming, along with more features and paid versions of the app. Expect this service to grow into something big, unless it gets scooped up by Google, Apple, or Microsoft to enhance their email offerings.
Tappin and Talkin from my iPhone 5