It's definitely a weird PSU.
Advertised with three 12V rails, all running at 18Amps, the picture I saw had 504W under one of the 12v rails, and nothing under the others, so I'd say that 504W is the maximum for all of them, with that, it seems like the each 12v rail runs on 14Amps.
I mean, yeah it should run a 1070, if it has a 6+2 or 8pin it should work.
It is definitely weird that the made it a triple 12v rail unit, if that's actually true.
I don't think it's a good PSU though.
Here's the link to the PSU :
http://www.gigabyte.com/Power-Supply/GE-P610A-C2#sp