This spacehopper has not been used for many, many years and has no air left in it, but my daughter used it when she was quite young and we don't think it has any holes, so it should inflate. It doesn't have a valve so you don't need a special pump, probably just strong lungs. The stopper keeps the air in effectively.
The word on it in yellow is "bounce".
I have rinsed the dust off it, but it could do with a clean. Looks dirtier in real life than in the photos.