Can't read the label but looks like Acrylic. A few cleaners in the past have had odour problems with this type of rug. Think its down to the latex glue degrading.
If a dog's definitely peed on it, the rug needs immersing in a sanitising/deodorising kind of product.Give it a good couple of hours' soak, then hose it off.What's the rug worth? You could be doing £100 worth of work on a £50 rug.The issue with latex smelling that JK mentions above (think it's called off-gassing??) is very distinguishable from urine, it just smells rubbery, so you shouldn't get the two mixed up. One tell-tale sign of that is sometimes if the rug's been on a light coloured carpet, the carpet under it might have gone a yellowy colour. People sometimes mistake this for UV fading on the rest of the carpet.