First, you should ask them again, but nicely. Often, the papers / projects are "administered" by Ph.D. students, who after graduation loose access to the machines on which the data might be. They might also no longer have an institutional email and their supervisor might have difficulties getting to them. Thus, getting the data to you might not be quite trivial and involve some work. An explanation why you want the data is therefore more than appropriate.
You might seek someone out that is more senior and commands more respect to intervene for you.
If you really want their data and they do not oblige you:
In academia, you can contact their department and school. In industry, you can contact their PR people and their supervisors. Promising data and not giving them is somewhat close to plagiarism. If the threat of a committee will not work, it will take a long time in academia for a committee to report their findings and even longer for any reaction.
You can also check whether any one of the authors is a member of a professional society that has an ethics statement. Not keeping promises could lead to sanctions.
Many funding agencies (e.g. NSF) will have a data availability policy for funded research. They will not be glad to hear that one of their fundees is taking data availability statements too lightly. Losing access to funding is a very serious threat.
You can also write to the editor of the journal. They have more standing in the field. If the editor of a journal that publishes them is angry, any author will reconsider.
You might also have legal recourse. After all, the data availability statement is a type of public promise that can be enforceable. Starting a lawsuit will get the attention of the legal team of the hosting institution.
Finally, administering data is not simple, especially when there is churn among the administrators (e.g. graduate students) and things get forgotten or lost. In this case, there is not much recourse. You might get an admonition and shaming of the leader of the group, but not the data.