Cage was playing around with numerous ideas. In a way, he was a scientist, asking questions of the seemingly obvious, so we realized it wasn't at all obvious.
For example, most traditionally notated music is timed by meter and tempo. Music is divided into bars of a certain number of beats, and played at a certain number of beats per minute. I saw a Cage piece performed that used a timer rather than meter/tempo. Music was performed as written during intervals specified by the timer. Some sections offered barely enough time to play what was written. Other sections might have three notes in thirty seconds, giving the performer a lot of say in the feel just by when the notes were played. So using Frank Zappa's formula that "Music is a way of decorating time", Cage was playing with the necessary relationship of time and music.
His prepared piano pieces questioned the nature of the instrument. First, question how it is played. Why do you have to play the keys? Can't you reach in and touch the strings directly? What does that sound like? Next, it questioned tone. Pianos are designed to be tonally consistent across the range - in a well-tuned piano, all the notes sound similar except for pitch. By placing objects on the strings, he could make different sections of the piano sound different, opening up new realms for composition.
Cage found many ways to inject randomness (as opposed to improvisation) into his compositions. The works for radios, mentioned in the article, are a good example. The composition is precise, but the results of performance are wildly unpredictable, and not reproducible.
So despite the fame of 4'33", and its intent of making the audience listen to their surroundings, Cage explored the nature of music a great deal more than just that one thing.