I'm familiar with most parents chatting at the playground, lessons, sports, etc with whomever brought the kiddo(s) that their own child is playing with (for example: nanny, parent, etc).
Often a compliment or two on how nicely the kids are playing is a good ice breaker.
Many parents are leery of strangers in the park, and conversation may move toward establishing who they may know in common... through pre-school, school, park & rec programs, library programs, lessons, sports, church/temple/synagogue, etc.
Mentioning that their child seems bright, might invite further conversation. Mentioning something you found interesting on Hoagie's may be a great way to bring up gifted without mentioning the G word.
Inquiring whether they come to the park on a regular schedule, because the kids seem to enjoy each other's company, would not be uncommon.
Exchanging contact information might be less common if you've not established knowing a mutual friend, co-worker, etc, because we are simply living in creepy times and is not unheard of for someone to stalk a person, break into their home when they are known to be gone (such as to the park), etc.
Just my 2 cents.
