Lots of people don't check in online and will check in at the airport. I don't think that portion of it is particularly relevant.

Was there a check-in email received 24 hours prior to departure? If so, that should show the updated times, and it'd be prudent to always check that to make sure there's no last-minute change. Delta should've contacted you or your parents earlier, but ultimately there's no clear legal issue (Delta's almost certainly in the right legally) and so any compensation or exceptions to policies for missing the flight would be goodwill measures on Delta's part.

In the future, it's always good to check upcoming flight bookings every few weeks, even if you haven't gotten any emails. Airlines don't always notify of changes, or maybe it gets caught in a spam filter or something was misspelled somewhere along the line. It also gives you a chance to handle the rebooking before the day of the flight, should some other itinerary other than the auto-booked one be preferable, or to try and get a refund and rebook on another airline should there be no more good options on the airline you initially booked with.