This article and the science behind it at this point is making some very interesting assumptions, such as that the Universe is closed (like the Earth is in their analogy).

But I believe at this point, the real answer is that we don't yet know. We're looking at a universe that looks flat and basically saying "well, it could be flat and finite, or it could be closed and curved, or it could be flat and infinite... but last time we thought our plane of existence was flat we ended up way off, so we better not make that assumption again."

Point being: take this conclusion about the size of the Universe with a grain of salt.

As an example of a flat but finite topology, think of the game "Asteroids" where, if the player's spaceship flies beyond the edge of the screen, it reappears at the opposite edge. This topology actually forms a torus! And, even though a torus definitely seems curved when embedded in 3D, its surface is actually flat - the angles of any triangle drawn on the surface always add up to exactly 180 degrees.

Cosmologist do usually take a flat universe to indicate an infinite universe. They also take "negative curvature" to indicate an infinite universe. Only a universe with "positive curvature" is taken to indicate a finite universe.