While coding a small project is a good idea time constraints can often severely limit what you can do. The reason companies ask a series of micro-questions (like Fizzbuzz or "implement a linked list") is that it lets them test a wide range of areas that they're interested in. If you're swapping that for a bigger project there's the risk you might find the candidate spending a lot of time doing one thing without testing them in other areas.
The particular way they're doing it is also a legal nightmare. If they use an applicants work there's a good chance that applicant current employer might have a claim over that code. Even if they don't use the work, but later build something similar themselves what's stopping the applicant suing them over it ? - it's not going to happen today, but if your startup is successful one-day you can bet you'll face lawsuits. Essentially you should avoid having the candidates work on something directly related to your product.
Also if you're going to take this approach it's a good idea to have a standardized project that every applicant does, both because it ensures fairness when you're comparing candidates and because it's much easier to defend if you face a discrimination lawsuit.
The particular way they're doing it is also a legal nightmare. If they use an applicants work there's a good chance that applicant current employer might have a claim over that code. Even if they don't use the work, but later build something similar themselves what's stopping the applicant suing them over it ? - it's not going to happen today, but if your startup is successful one-day you can bet you'll face lawsuits. Essentially you should avoid having the candidates work on something directly related to your product.
Also if you're going to take this approach it's a good idea to have a standardized project that every applicant does, both because it ensures fairness when you're comparing candidates and because it's much easier to defend if you face a discrimination lawsuit.