Typical non-eligible stay is a room booked through Priceline, Expedia or any other discounted rooms which require prepayment at the time of a reservation unless you booked through Hyatt.com.

As long as you made a reservation through Hyatt.com or Hyatt's phone reservation line, your stay at Hyatt Place is an eligible stay.

Being Platinum is definitely better than being Gold, but I don't know whether worth it or not.