I think this will expresses strong desire or determination. According to your link (Dictionary.com), I think will 2, senses 9 and 10 are quite close to the intended meaning.
verb (used with object), willed, will·ing.
9. to decide, bring about, or attempt to effect or bring about by an act of the will: He can walk if he wills it.
10. to purpose, determine on, or elect, by an act of will: If he wills success, he can find it.
The next paragraphs in that post (USA TODAY) make it quite clear that she really needed a strong will to succeed in this French Open.
She was pushed to three sets in her last four matches but never folded, always finding a solution and an extra gear. [...]
Against Halep, she needed to go the distance again.
The final match was 3 hours and 2 minutes long, and obviously not easy, but she prepared herself for it as she said a few days before the match,
"I would love to win those matches in two sets, but I always feel like I put in the work to be ready to play whatever it takes. If it takes three hours to win the match in three sets, I will be ready for that."
As an aside, the phrase "verb one's way to ..." is also interesting. It seems like you can apply almost any verb to the phrase. For example, besides something obvious like making your way to your bedroom, you can sleep your way to the top, work your way to success, trade your way to financial freedom, laugh your way to a better marriage, talk your way to the top, think your way to a better life, and obviously, will your way to the title.