Is this gas in thermodynamic equilibrium?
I don't think "equilibrium" is a good word to use in your question.  We have no way of knowing if the gas is at equilibrium from the data you present.  A highly non-ideal gas that was exploding might give the same relationship.  A gas undergoing a rapid unimolecular reaction wouldn't really be at a true chemical equilibrium but could behave as an ideal gas from a pressure / temperature standpoint.

Did you really mean to ask if the gas was ideal?  An ideal gas follows $PV = nRT$, which can be re-written in several ways:


molar density $\frac{n}{V}$ as a function of pressure $P$: $$\frac{n}{V} = \frac{1}{RT}\;P$$, which is the equation of a straight line through the origin (bottom graph).
molar volume $\frac{V}{n}$ as a function of pressure $P$:  $$\frac{V}{n} = RT \frac{1}{P}$$, which is the equation of a hyperbola (top graph).


Your data is consistent with the gas being ideal (and isothermal).