What makes someone a true piano player. It doesn't matter how many awards, you have, or really how accomplished you are. What matters is your musicality.
The simple answer is, "No." If you want to accompany other musicians, you probably should become a good sight reader. If you want to play in a rock or pop band, you should probably learn to play by ear. If you want to be a good jazz player, a solid understanding of theory will make your journey less frustrating. If you want to be a great classical artist, you will need to get good at memorizing music. But there are great musicians who lack one or more of these skills and still manage to make wonderful music. Pursue the skills that support what you want to achieve musically.
These are all learned skills, and I believe that anyone who truly wants to learn them absolutely can. Desire (passion, drive, etc.) is ten times more important than talent. Productive, focused learning and practice habits are ten times more important than how much time you put in. But you still have to put in time, and there is no getting around that investment.
I have a friend called Nicholas without any experience on playing piano, he start from learning the notes and keys, working harder than anybody who has experience. Until now, he got the skills. Every body will say why do you so obsessed with playing piano, and nic will say” because i love it, im enjoy to learning it.”
The important thing to keep in mind is that we aren't born with the ability to play by ear, or to be good at sight reading, or memorization. Certain musical skills may develop more easily for some than others for various different reasons, but nobody gets there overnight without effort. If you really want it, then work hard at it. Focus every minute of your practice sessions on stretching and pushing your brain to it's limit. Every note should be a learning experience. It takes a lot of energy to maintain that kind of focus, so start small. With intense focus on learning, you can achieve a great deal in 20 minutes, 3 days a week. Some people spend hours a day going through the motions and never get very far. It's the equivalent of leaning on a shovel while daydreaming, and then wondering why the hole isn't getting any larger. This ultimately leads to the common excuse: "I took lessons for two years and I'm just not musically talented." Don't be an excuse-maker. Don't ever tell yourself you can't do something, and don't listen to someone else who tries to limit your potential by suggesting you just don't have what it takes. When that happens, just think to yourself, "Challenge accepted." And then prove them wrong.