First of all, that area is chock full of deer. The rut is kicking in and some of the young bucks are on their feet moving around seeking and chasing. People run their dogs off leash there all the time. Not to say that is appropriate.
The dogs didn't hurt that deer. Heck, the lab is lucky it didn't get an eye gouged out.
Btw, slightly off topic, this area where this was filmed holds some of the biggest bucks you ever seen. They have been protected for years until they paid some snipers to come in and clean house last year. Too bad they didn't open it up to bowhunters and save a boatload of taxpayer's money. No, that would make too much sense.