According to Wikipedia:
"An ideal gas is a theoretical gas composed of many randomly moving point particles that are not subject to interparticle interactions".
But suppose that two boxes of ideal gas at different temperatures are placed side by side and the separator septum is removed. In the end we will find a gas at an intermediate temperature so the molecules interacted. How does this agree with the definition given in Wikipedia?
The answer is written a few lines later: "The requirement of zero interaction can often be relaxed if, for example, the interaction is perfectly elastic or regarded as point-like collisions".
The gas molecules can indirectly exchange energy through colliding with the box wall. Suppose a hot particle collides with the left wall of the box. This will make the particle transfer a slight leftwards momentum to the box and become colder, and then a cold particle colliding with the right wall of the box may gain a part of that momentum and become hotter.
Of course, if the box is rigid and infinitely heavy, this heat transfer mechanism doesn't exist, and you may indeed get a mixture of ideal gases with a non-Boltzmann velocity distribution, that never thermally equilibrates. But since almost no discussions on ideal gas thermodynamics assume that the box is infinitely heavy, there is no contradiction between most thought experiments on ideal gas thermodynamics with the definition of the ideal gas.
