Definitely not screws. I use these push in terminals all the time where I work. If the wires were always being tugged on then yeah, soldering or screw terminals, but these are just sitting there.
I just installed one I got from Xpin's site into my EK. Heck of a lot easier than soldering onto the bottom of the board. The original was so roasted I had wires on top of traces and wires from the connectors soldered to the board because the pins were gone. Total mess.