Yes just like humans can pull a groin muscle a dog can also pull a groin muscle accidentally especially during active play and running.
The groin muscle is one of the muscles in the iliopsoas muscle group and it certainly can be injured and pulled when the dog is really active.
If you think your dog has pulled a groin muscle then you could take the dog to the vet if you can and have the vet look at the dog and see whether or not the dog has actually pulled the groin muscle.
But usually just allowing the dog to rest and and giving the dog some pain medicine such as aspirin can usually work to help the dog heal the pulled groin muscle.
If the dog will allow you to you can place an ice pack on the area where the dog pulled the groin muscle which will help with the inflammation.