Saying property rights don't exist because they can't be touched (or as some would say, because they have no shape) is to not recognize that many abstract ideas exist despite not being tangible, e.g., families are more than the people who comprise them; they are also the relationships between the parents and children and other members of the family. Qualities and relationships are as much a part of existence as tangibility.
I have doubts that property rights exist in any form. What does exist, as a relationship between a person and a thing, is ownership.
One can't own an action. An action is not a thing. One can be responsible for an action, of course, but that isn't the same as owning. One can't sell or buy an action. If he could, then the buyer would own the action and be able to do with it as he pleases. One can pay for a service (e.g., an action), but the service isn't owned by the person who receives it, even if said person does own the result of the service or action, such as a haircut or house-cleaning.