airtime is time spent "on the air", whether that be on a TV network's broadcast spectrum or on a phone network's spectrum.
There's nothing in the meaning that has anything to do with money.
That definition is akin to defining food as "the sustenance you pay for at the supermarket". That definition might make sense for groceries.
free airtime is like free food. The phrase is meaningful in contexts where you would normally have to pay. A separate definition "the amount of time that is paid for when you are using a cell phone" is not required by the fact that many phone plans allot customers a limited amount of airtime for the money they pay to the phone company, or by the fact that you have to buy food at the supermarket. Sometimes I think that advanced learner's dictionary must have been put together by advanced learners. In any case, learner's dictionaries are less interested in lexicography than in being a Baedeker for "visitors" to the language.
With respect to "30 minutes free airtime" it is quite common to have units of measure like "30 minutes" or "10 days" quantify a thing without partitive of.
He needs ten days rest after such an illness.