Claiming a recording IS real music is analogous to saying a photograph of my dog IS my dog (without the fur :-). Really not the same thing at all.
No not at all. It comes down to your definition of music and I choose to agree with Wikipedia’s. I don’t know who’s definition you are using.
From Wikipedia:
Music is the arrangement of sound to create some combination of form, harmony, melody, rhythm, or otherwise expressive content.
Music may be performed using a wide variety of musical instruments, including the human voice. It can also be composed, sequenced, or otherwise produced to be indirectly played mechanically or electronically, such as via a music box, barrel organ, or digital audio workstation software on a computer.
There is nothing to say that the sequence of sounds must be produced "on the fly" and this last paragraph would include recorded music which is indirectly played.