Whichever version of the idea you read, I believe nobody could master (not ‘be very good at’, but ‘master’) a subject (or a game like chess) without a significant amount of deliberate practice. What I am less sure about is whether the same amount of practice leads to the same results for everyone. That means that I don’t put much faith in the mythical 10,000 hours (a figure created by Gladwell; since largely debunked) to become a master. It may be a ballpark figure, but it is not THE figure.
In this article in The New Yorker, Maria Konnikova describes the work of Zach Hambrick, who suggests that practice plays a role, but is not nearly the whole story. Genes, work ethic and environment are just as important.
An interesting read, but I for one will be careful not to use a lack of the correct genes, or the correct environment when I was younger, as excuses for not progressing. I will continue to practice deliberately, work deeply and focus on my process goals. I may never master chess, but a very large number of hours of deliberate practice may just help me on the way.