You should do a search about these, but I am sure with the Delta promotion this forum will be deluged by newbies trying to figure this program out and being totally confused between PRIORITY CLUB and AMBASSADOR elite.
However, to answer your question, experience over the years starting with the same certificates issued under the old SIX CONTINENTS CLUB program, say only rates booked through IC res or on the PC internet site qualify. All other industry and promotional rates do not. [Nor have I ever seen an INTERCONTINENTAL HOTEL included in an Entertainment book.]
Since the lowest rates on the web require a non-refundable deposit of the full cost of the stay, many have booked their second weekend night by confirming the first at this low rate, then booking a second reservation for the next night at the lowest rate that doesn't require prepayment or have a cancellation charge of $25. They put a note in the comments box that this second stay is in conjunction with the initial cheaper booking, quoting that confirmation number, and that you will be using a 2nd Wkend Night Free certificate. When you check in for the prepaid night, show you second res to the desk clerk and they will combine the two. The certificate is then used to "pay" for that second night.
And remember, this certificate is only good at INTERCONTINENTAL HOTELS & RESORTS and NOT other IC brands like HOLIDAY INN, CROWNE PLAZA, STAYBRIDGE INNS, etc.