Very close. The first beat comes in a little bit too soon to be 7/8... try tapping it out and you'll notice. Tapping with your first two taps on the first two drum hits will get you the right tempo.
The reason that it can sound so close to 7/8 is because 7/8 = 14/16, which is only one sixteenth off of 13/16.
13/16 still isn't perfect. There is something like an extra quarter beat every measure, as in 13.25/16. Of course, that makes it closer to 13/16 than 7/8.
The reason that it can sound so close to 7/8 is because 7/8 = 14/16, which is only one sixteenth off of 13/16.