I doubt this is a response to ADP; ADP is a horrible product, and Zenefits knew they could make a better solution (like ZenPayroll/Gusto). They've probably been working on this for a year, to be honest, given the requirements for payroll providers and syncing with the IRS/etc.
What's more interesting is that the payroll is free only if the company manages everything else HR related in Zenefits. Talk about lock-in.