Is piece work legal?

In the state of WA is it legal for an employer to pay an employee piece work? For example this guy wants to pay my DH $3 a square foot to install granite countertops.
He has been told that he would need to have a business license to do this.

Sounds like the employer wishes to hire your husband as an independent contractor, not an employee (hence the need for a business license.) Your husband should clarify exactly what employment status is being proposed by this company.

P.S. Either way, yes it's legal to pay your husband by the piece provided that the piece rate results in his being paid at least minimum wage IF he is an employee. If he's an IC, then he can be paid on any basis the two parties agree to.