The first one we'll start with is Graphik (the font used on their cover) which can be bought through commercial type and was designed by Christian Schwartz in 2009. Esquire uses it on the cover and throughout the issue for categories like "Style", "cars" and "MaHB" (Man at his best). It's a very nice font, modern and bold,very easy to use as well as easy on the eyes.
The next one is Granger, which was commissioned by Esquire from Commercial Type. The name of the typeface was for their long-time editor in chief and was designed by Kai Bernau and Susana Carvalho. Granger is also used as one of their pillar typeface with Graphik throughout the issue and is quite prominent. Both those fonts stand very well together and bring the layouts together nicely.
Now the last one I'll cover today I am not sure about. They use a condensed type on their cover which I would assume after digging around, is Giorgio Sans from Commercial Type. It's a very nice typeface, lots of different weights, very modern and simple. It goes very nicely with Graphik and Granger, so nicely actually you almost don't notice there's a third type family on the cover.
I will keep updating this post as I get more info so stay tuned!