I made a zigzag quilt using the same tutorial and I cut my corners off, it looks fine. I get a lot of compliments on it. I used the parts I trimmed off to piece the backing.
If you want to keep your zigzags, you could piece in some setting triangles. Or, you could keep the top as is, layer and quilt it, then trim the backing and batting out from between the zigzags, and have fun making a zigzag binding!