Help understanding how to remove faucet with perpendicular pipe sticking out
I suggest that you should remove the faucet handles and take a look from above. Most likely you remove a small cap at "A" and reveal a screw that when taken out permits the faucet handle to be lifted off. 



Once removed there may be a nut or ring clip that is normally covered by the "B" skirt of the faucet handle. Removing that nut or clip ring would allow the rest of the faucet assembly to drop below the sink.

The center water spout part of the faucet assembly most likely does need to be freed from below and then pulled up through the top of the sink. You would would need to take apart that 4 way pipe fitting assembly that all the hoses are attached to and then use a basin wrench (as suggested in another answer) to loosen the large nut up around the center hole part of the sink.

Note that if the faucet units have ring clips it may be necessary to also loosen their large nuts from underneath so that the ring clip can then be removed. Usually when these types of faucets are initially installed the large nut is pre- threaded  down on the unit toward the right angle port where the hose attaches.Then the thing is shoved up through the hole, the clip attached, and then the nut underneath is tightened up to the underside of the sink to secure the valve unit in place.