All vining crops in the square foot gardening system are grown vertically. This includes squashes, melons, tomatoes, pole beans, pumpkins, gourds, etc. The thinking is crops get better air circulation and better sunlight. Another benefit is that it keeps things off the ground making it more difficult for pests to ruin your crop. You also don’t have to worry about turning an ankle because you didn’t see one as you moved through the large leaves they have. 

I’ve posted before on growing zucchini vertically in one square foot. It works and I’ve been doing it for years. This is a picture of angel hair spaghetti squash. Right now there are 6 growing, with one ready to harvest in about a week in the lower left hand corner. There’s probably only 10 pounds of squash growing at this time but in several weeks, this will be a wall of green filled with a lot of squash. And all it took up was 2 square feet.