Is there a playground in this park

Yes

There is no park. Shirley consists of paths and fishing areas, as well as picnic areas.

I didn't see one this week.

Actually in the actual park there is no playground at this time.Its a park focusing on nature and relaxation.You can bike, hike or walk or sit down in the picnic area. https://parks.ny.gov/parks/shirleychisholm/details.aspx