There's already a thing called "likeness rights" that actors have. Presumably the filmmakers in this case made a deal with whoever inherited those rights when James Dean died.

The article has a bit on this:

In general, when a celebrity dies, "rights to publicity" pass on from the celebrity to next of kin, or to the party granted these rights in a will. But Kahn says even a will, which will usually dictate who will benefit financially from the commercial use of the dead celebrity's image and likeness, holds limited legal weight since "it's not like a contract because it's a one-way document". The power for how that person's image is used passes to their living executor.

People need to realize that dead people do not have rights, only living people have rights. A dead person can't go to court.