All the greyhounds we have had are fantastic with cats that they know. But I would be really worried about strange cats in the distance out in the open, because of course greyhounds are trained to chase dome small furry things. RÚnan pictured there is not afraid of cats. Our current Ciaran is afraid of one cat, Orange aka Tiddy Puss because Orange used to keep whacking the greyhoundsí backsides when they went past him, either just to hear them yelp and run, or to prove he is top cat, or else because they had insulted him by not saying hello, because the latter has been known. It was always just as the dog was going past Orange's Hugh vantage point, so I suspect he might have already been offended. Some of our cats will whack the dog if they don't get any greeting / rubs / fuss from the dog. The cats expect the chance to rub round the dogs' legs or nuzzle their faces and some of them are really angry if ignored, you can see the catsí faces go dark with fury.
That having been said, RÚnan would not normally have been that brave - he would have got up and cleared off - but I think he was fast asleep and never knew anything about it, and Buidheag /bujak/ just took advantage of him as a nice warm cuddle. Buidheag loves dogs a lot. So does orange when he is not whacking them.