yes - you'd have to purchase park passes with both reservations in order to have dining for both stays.
Because WDW park passes get cheaper the more days you add to one park pass, it can mess up a budget to have to buy park tickets for two separate stays.
The package reservation can be purchased with as little as a one-day base ticket per person, but you do have to buy theme park tickets to get free dining. If the free dining stay was first, you could buy tickets to cover the entire stay with that package - but since it isn't first you definitely have to buy tickets twice, unless you don't need park tickets for the first three nights.
Your check-in date must be August 16 or after for free dining so you'd have to split into two reservations. They won't extend dates at the beginning of the promotion.