Beats tend to consist of four to five elements of music. In that way they really are no different than any other genre of music. You have the drums, the bass, the harmony, and the melody. Maybe some little transition sounds and springs but in general the core part of the music is the same. So then the question is, what makes a beat a beat? What's the difference between a body of music that is the background of a soul song and a body of music that is in the background of a rap record? They all contain the same elements but one is referred to as a beat and one is not. At first glance you could say that a beat is recorded with synthesized sounds such as keyboards, drum machines, and softsynth plug-ins for your computer. A soul music bed would contain all live instrumentation. Live drums, live bass, live strings etc. While this is true there are plenty of examples of beats that utilize either parts of live instrumentation or are recorded entirely live. Producers like Kanye West and J Dilla routinely would hire out musicians to add a live element to their music. Also groups like The Roots record beats that are one hundred percent composed with live music. So why would their music be referred to as beat while music of other genres would not.
The main thing that classifies a beat as a beat is the repetition within the music. Beats tend to repeat themselves every two, four or eight measures. The chorus and chorus build up tend to just add layers on top of the foundation of the beat that stays constant. Beats have more of a driving energy that the listener consciously recognizes. That's the thing; beats are not only in reference to rap music. There are plenty of examples of beats within other genres of music. Funk music has funky loose beats or grooves, house beats and many other kinds of electronic music all refer to their music as beats.
The main thing that differentiates the beats from non-beats is what is the main driving element of the music. If it were the groove of the drums and the bass then you would probably refer to it as a beat. If it has no drums then you most certainly would not be referred that way. Music like classic rock would have a heavy groove to it but the focus is not in the way the drums and bass work the focus is in the harmonies and melody. The groove of the drums just compliments that.
At the end of the day what a beat is and is not really is open to interpretation. I feel this way, others may feel a different way and really there is no right and wrong. All we should really be focused on is how the music makes us feel. If it strikes the right chord with our minds then who really cares what you call it.