With Science. First let me define what is considered to be running:
1/ You have intermittent contact with the ground from one foot to the other with a flight phase,
2/ fluctuation of kinetic and potential energy,
3/ body orientation, height and speed are stabilized.
OutRunner clearly demonstrates all these points:
1/ the robot is stepping from one foot to another and has a flight phase without ground contact, this is highlighted in the video where the robot is running with 4 legs only.
2/ Legs are spring loaded, this allows for storing the potential energy (due to gravity pulling the robot down) into springs which then restore this energy into thrust (kinetic energy), allowing the robot to move forward. That's one of the reason the robot is so efficient and can run for 2 hours where a RC car equipped with the same battery will work for 10 to 20 minutes at best.
3/ Body orientation can be decomposed around three axis: yaw, pitch and roll. Body pitch is stabilized by the buoyancy effect we are talking about in the "How does it work" section. The gyroscopic effect provided by the legs spinning helps stabilize yaw and roll but that is not it. You'll notice in the front view videos, the robot yawing from left to right and vice-versa with each steps, similarly to a human running. That demonstrates that the ground reaction forces coming from the foot in contact with the ground are pushing back the robot to a neutral position, allowing him to run straight.
Speed and height are also stabilized, you'll notice in the video that the height of the robot doesn't change much and it's able to maintain a constant speed.
Now what about steering? if you want to turn with two wheels, your only solution is to have one wheel spinning faster than the other. In our case that won't work. What we do is to actively shift the center of mass position of the robot with a servomotor to redirect the action of the ground reaction forces, forcing the robot to lean on the side which induces a turn, which is one of the mechanism similar to what bipeds do when they turn.