You'd be surprised - for a number of musicians it's not about sight reading notation and playing fom there, it's about developing musical talent and variations and adding in formal notation reading | writing later.
I've known a family of three siblings who all played in the state orchestra in their teens and only one was a fluent reader, the other two were extremely good musicians that practised hard and either very slow worked through written music note by note, or, once familiar with a piece looked at a page of music with a helicopter view, not reading" individual notes, but tracking off entire blocks .. like seeing a page of text w/out wearing glasses.
From the same music roots, some years later, Tim Minchin- admittedly more an Entertainer than a pure Musician - but none the less someone that made their name and living from performing original and relatively complex music on stage playing piano and singing - also doesn't read music:
I used to play in a couple of competitive bands, I always ended up in 1st / 2nd chair, but I always started in lower chairs because I can’t sight read music and would botch my auditions.
Once we were in the room and playing, and I got to hear the music, I was good and the notes on paper made sense- but out of context the notes didn’t do it for me.
Doesn't read | write sheet music (see youtube interview linked in GP comment)
Oxford English Dictionary:
musician - A professional performer of music, esp. of instrumental music.
Wikipedia:
Timothy David Minchin is a British-born Australian comedian, actor, writer, musician, poet, composer, and songwriter.
Also - pretty much the entirety of Indonesian traditional ensemble musicians (Gamelan and other) going back to the bronze age - no sheet music so no reading writing music - they train like Homer delivered poetry and use non Western scales - their music is available in notation, but notation created by westerners.
Here's a bit about Western students learning to learn music w/out using sheet music ...
Many of the greatest jazz musicians of the 20th century didn't know how to read music, and jazz is rather famously considered overly complex and obtuse for the typical listener. Notation is useful, but it is not music.
The volume of fairly famous or otherwise well-established musicians in rock, funk, and even jazz with a poor or non-existent ability to read or write music notation is not insignificant.
Then there are all the non-western scale musicians who learn other systems, or use some variation of solfège to explain musical ideas.
I'd say Michael Jackson was a musician given I'd never seen his videos but loved his music as a kid and still do. Dude did his own compositions & simply sang the parts to other musicians.