This is a rather unusual use of the word 'eligible'. I have not heard it used in this particular way before.
As you suggest, I think the main eligibility for 'buying' a car is that you have the money to do so, although some countries may well have age conditions related to the purchase of a car.
Of course, depending on age and and qualification, you may not be eligible to drive the car, buy the car with a bank loan, insure the car, or register it in your own name. (This depends on the local regulations which vary from country to country and state to state).
- She is eligible to drive the car, now that she is 17 (in the UK...) and has passed her driving test.
- Now she is 18, she is eligible to apply for a bank loan to buy a car.
But wait,... I have just found this ☹️:
"In addition to most purchasers needing to prove they have owned Ferraris before, age can be a factor as well, as many dealers won't sell to purchasers 'under the age of 40'".
13 Dec 2020.
Great news!!! - I am now eligible to buy a Ferrari... 😁😎👍