How to prevent a cookie from becoming spongy like a cake?
They're definitely under cooked. The recipe calls for a 10 minute bake at 350 degrees -- that's seems short. You want to pull them when the edges are darker brown, which probably would have taken another 4-8 minutes.

It's hard to tell with the lighting of your photo, but I think your tops weren't browning fast enough either. Before I got a new oven, I'd have that same problem when I baked cookies. I fixed that by starting the cookies on a lower rack (one or two slots from the bottom) and moving them halfway through to a higher rack (one or two slots from the top).

Letting the cookies cool on the pan also helps set them hold together better.

EDIT: As for the texture -- you aren't going to get a crunchy cookie from this recipe. This recipe is for a slightly chewy cookie with crisp edges. If your cookie is still cakier than chewy, you may want to make sure you are measuring flour correctly.