This is a big vine, but not invasive or destructive, You should be able to keep it in check with regular pruning. The great news is that is not toxic to your dogs just in case they decide to do your pruning for you. Many other vines are not safe to screen dog runs. My sister-in-law's most reputable landscaper planted Carolina Jessamine in front of her dog fence. Bad choice as a small nibble will kill an adult goat.

Hops can spread by underground rhizomes so I would consider it to be a very enthusiatic grower. I had the variety known as Golden Nugget and it got out of control within two years and as a result I killed it off by digging up as many of the rhizomes as possible and spraying anything else that came up with Roundup. Mine was in an uncontained area so you might get away with it in your situation but just be on the look out for it popping up in unexpected areas.

My sister grows hundreds of variety of Hosta. She has a huge honeysuckle hedge line around her property. Her neighbor planted hops on his fence two years ago. It is now in her Hosta's and is just taking over. She's at her wits end. She has said something to the neighbor and he doesn't think it is his problem. Make sure it isn't something that will hurt any body's yard around you.