Scientist use models to try to understand and predict behaviors in the world. These models can be broadly classified into two types: empirical and physical. An empirical model is one that simply seeks to provide a mathematical relationship between different properties based solely on observation. The combined gas law is an example of an empirical model that is a relationship between the properties of volume, temperature, and pressure for a gas. Based on the combined gas law a chemist could predict the pressure of a known amount of gas given its volume and temperature. A physical model is different in that it seeks to not only predict but to provide some physical insight. The Kinetic Molecular Theory is an example of a physical model. It starts with some assumptions (the particles are small and non-interacting, the particles are in constant motion,...) and then from there seeks to derive a relationship between the properties. In this case, it happens to derive the identical relationship that we refer to as the ideal gas law.
We can therefore either look at the ideal gas law as an empirical model derived from observation (combination of experiments from Boyle, Charles, ....) or a physical model derived from kinetic molecular theory. It is more useful to think the ideal gas law from the perspective of a physical model. This is because one of the most important aspects of models is the insight we gain from their failings. Many scientific models start by simplifying the behaviors observed in the real world. By testing the models versus real data we can see when the assumptions of the model are valid and when the simplifications they make should be called into question.
For example, what do we gain from the fact for typical conditions (1 atm, room temperature) the ideal gas law does a remarkable job of accurately predicting the relationship between the volume, temperature, and pressure of essentially every gaseous substance? This is a remarkable feat. Why should Xe behave like N2? Why should acetone vapor behave anything like ammonia? The fact that all substances appear to be the same is a validation of our small particle kinetic molecular theory model. The KMT model assumes that gas particles are non-interacting and derives the ideal gas law. Non-interacting particles means that the molecules have no intermolecular forces. They are not repulsive nor are they attractive. When the model is correct, its assumptions must be valid. The ideal gas model assumes there are no interactions at all and it predicts the correct behavior (in most conditions). How can it be possible that there are no intermolecular forces? In a gas, under conditions where the ideal gas law is valid, the particles must be sufficiently far apart that they are in fact non-interacting.
This would suggest two conditions for which gases would not behave in this ideal non-interacting fashion. First, when they get very close together. Second, when their intermolecular force are very strong.