Identifying an ideal gas

The gas you are describing is not precisely an ideal gas, but is pretty close. In an ideal gas, the molecules are dots, they don't have volume ; moreover, threr are no interactions except for the elastic collisions that allows the gas to thermalize.

The gas you describe is is a gas with no interactions, but with molecules of finite volume. Having molecules of finite volume reduces the space avaliable for molecules to move around, hence the $V-b$ factor instead of just $V$ for an ideal gas.