Basically the whole example (http://matplotlib.org/examples/api/custom_projection_example.html) seems to be an outdated implementation of the Hammer projection (available at https://github.com/matplotlib/matplotlib/blob/master/lib/matplotlib/projections/geo.py). In fact it is so outdated that it doesn't manage to make the lines become "curved" like they should. Instead, just copy-pasting the if __name__ == "__main__" block at the end to use the standard hammer projection results in a correct plot:

import matplotlib.pyplot as plt

plt.subplot(111, projection="hammer")
p = plt.plot([-1, 1, 1], [-1, -1, 1], "o-")
plt.grid(True)

plt.show()