The answer is simple but the explanation behind the answer may be instructive. The simple answer is: the x-axis label should be read as (m/s)^2, not m/s^2.
The longer explanation is related to this bicycles.stackexchange answer. The power needed to ride at steady speed on a flat road under calm wind conditions is
Watts = Crr * kg * g * v + 0.5 * rho * CdA * v^3
where Crr is the coefficient of rolling resistance, kg is mass, g is the gravitational constant, rho is air density, CdA is the drag area (that is, the product of coefficient of aerodynamic drag, Cd, and frontal area, A), and v is the speed of the bicycle in meters/second. Watts are a Newton*meter/sec, so if you divide both sides of the power equation by the speed v (in meters/sec) you get the drag equation:
Watts/v = Newtons = Crr * kg * g + 0.5 * rho * CdA * v^2
Thus, if you know power and speed, you can plot v^2 on the x-axis against watts/v on the y-axis and you will get a straight line with intercept = (Crr*kg*g) and slope = (0.5*rho*CdA). This is what was done in the NY Velocity article describing the characteristics of the Lemond Revolution trainer, and is the "classic" way to estimate drag parameters of a bicycle from on-road field tests when you have a power meter. Other ways are described in the bicycles.stackexchange answer linked above.
Elsewhere, the "virtual" Crr and CdA of the Lemond Revolution were estimated using a related technique. Note that a graph is given where Newtons is plotted on the y-axis and speed^2 (that is, (m/s)^2) is plotted on the x-axis.