The dog is called Fenton, there are numerous threads on MN referring to this incident.
You can never be 100% sure that your dog will NOT 'zone out' and the poor owner was trying his best to get the dog back.
There was no harm done, nobody was hurt and Richmond Park is a massive area. The dear are lowing in the grass and can startle a dog and then they in turn run off and the dog cant help itself.
Vigilance is key when walking in an area like RP or other Royal PArks nearby.
To say "keep the dog on a lead" really isnt feasible.