I think this is a good lesson in how to convey in Portuguese the idea of the English. It's not "bird watching," which is a hobby or serious pursuit. It just means "when i'm sitting here in the park, I love watching the birds." It gives us another living example of how to use ficar.
Spanish has two verbs that translate "to be" in English. Portuguese has three: ser, estar and ficar. There is a good discussion here: http://www.nativlang.com/po/qg_verbs_serestarficar.htm. Hope this helps>