What is stolen is pretty fundamental, actually. It is their ability to receive compensation for their effort.
I was recently talking to a local locksmith who told me about a call he answered to help a person who had locked their keys in the car. When the person called, he told them it would cost them $43 to open the car. When he got there, he opened the car and the gentleman said, "That was very little work to open my car. I don't think that was worth $43 dollars." The locksmith's response? He tossed the keys back in the car, locked the door, shut it, and walked away despite the man's promises to pay his fee. He knew the man was going to try to pay him less than $43 and he preferred to take the loss than to encourage such behavior.
Now, using your amazingly strict definition of theft, that only depriving of their property qualifies, the man could have refused to pay the locksmith and that would not have been theft. Indeed, according the the logic of many people who complain that cost is the problem, the man should have been free to pay the locksmith whatever he thought the locksmith's effort was worth. Theft does not simply deal with taking the property of others but in taking benefit from the efforts of others without compensating them and by making it difficult or impossible for them to receive compensation from anyone. This is exactly why the Constitution explicitly grants Congress to make laws protecting inventions and writings.
There are three was that the song could have been stolen: 1) The song itself. The way intellectual property (IP) is stolen is by someone claiming it to be their own. Has this happend? No. 2) The medium itself. The way a medium (object) that contains the IP is stolen is by removing it from the owner, thus not allowing the owner to sell the medium. Has this happend? No. 3) The service. One can steal a service (like a radio song) by removing the ability of the radio station to play it and playing it themselves. Has this happend? No.
There are other ways that a song could be stolen. If a band is performing live a local venue -- they pay the rent and insurance for the venue, they pay for the utilities and equipment used in the performance, and they spend two hours of their time playing, and you sneak into the concert hall and watch the performance for free, have you stolen from the band?
When you buy a song, you are buying the right to enjoy a performance of that song, just as if you'd bought a ticket to a concert. Yes, you are listening to a recording that is trivial to duplicate without additional effort but you need to keep in mind all the costs and effort that went into creating that one studio recording.
The only value argument that could be used is a potential value argument (the owner lost a potential sale if the copy is created). However, creating a potential loss of value isn't illegal, and it happens all the time. In fact, it happens everytime competition gets the upper hand.
It is compensating the band for the labor of their performance and the time money they spend writing, producing, recording, and promoting their music. To say that they don't deserve compensation for their labor and expenses but only their property makes you sound very much like the gentleman who didn't think the locksmith deserved $43 because it only took him a few seconds to open the door. If you enjoy the benefits of someone elses labor, they deserve compensation if they seek it, and it is up to them, not you, to set a price on it.
You do believe that people should receive compensation for their labor, do you not? Or do you think that having people do work for you and then refusing to pay them isn't theft?