If you had furniture how would it be arranged? Purchase that size rug for the future.

If this is a 'dog room", then I would get an outdoor rug that you can take outside and hose it down to clean it.

I have no clue as to what this space is but with dogs no rug unless it is washable so look at ruggables I guess but we need info as to why this room cannot have furniture . If it is a dog room Chilewich makes great floor mats that are just hosed down to clean .Waht does the rest of the LR look like ?

What makes this room a "living room" as opposed to a "catch all room for the dogs"? First, examine the actual use it will receive.

A room with just a rug is perfectly fine. Just make sure you have a rug gripper underneath so it doesn't go sliding and the dogs flying when they run over it. I like chispa's idea for a indoor/outdoor rug. If this room is only used by dogs I'd even consider a large waterhog.

The photos show only about half the length of the room. the othwr half is where the living room furniture in it. its a very ling room.

There wouldnt be enough walking area (to get to stairs) if the furniture were placed across from the wood stove. its a very awkward room

Maybe this helps?

DRaw a floor plan with measurements and post pictures of all "4 walls"

IMO a floor plan becuase I see no reason for not having 2 seating areas one for TV one for the FP I have huge dogs they have to live in our space not an issue . I ahve avery large LR with 2 seating areas we do not however have TV in there . The dogs never go on the furniture in the LR, not sure why, but they sure think the media room furniture is a go

If the space will be dedicated to your dogs then as others have said - select a washable rug. These are some lucky dogs to have their own living space!