I agree that it sounds like Essie, who at 2 1/2 is still mentally very puppy like, was just wanting to play. I wouldn't let her interact with other dogs until you get to know her better and she has adjusted to home life a little more. I am not sure how long you have had her? One exception to that is, if you can find a greyhound only play group, or even know someone with one or a few greys and an area where you can let them all safely play off leash (muzzled, of course) you can better judge Essie's reactions. I would bet they would have a great play time, which can look scary to someone who has never seen greys play
As for the cat, did whoever you got Essie from say she had been cat tested and was OK with them? If so, do like Robin said and she will probably do fine. Make sure the cat has somewhere (inside) to escape to. I have a baby gate installed in the doorway of a spare bedroom, about 8" off the floor, the cats can go in there when they want to get away from the dogs, but the dogs can't get in.