Stop. Do not do any of the things you are thinking of doing.
The authors did not provide the source as a supplemental file, but
assure the reader in the article that it will be made available upon
request.
Have you thought that they need to polish the code before releasing it? The fact that I am planning to release my source code does not mean that I have to do it now or whenever suits you.
Pursuant to the guidelines for publication in the journal, "[i]f
published, software applications/tools must be freely available to any
researcher wishing to use them for non-commercial purposes, without
restrictions such as the need for a material transfer agreement."
I have seen journals like that in my area (CS). Still, this initial rule proposed when those journals came out, might atone through the years. Since in certain areas, conferences are the main publishing venue, journals sometimes "relax" their original rules to get enough submissions to get them going. So, I would not count towards this rule to pressure the journal or the authors of this work. Check out some other works on this journal. Do they actually released the code? If not, then releasing the code is the exception and not the rule.
Also, "software applications/tools must be freely available to any researcher wishing to use them for non-commercial purposes, without restrictions such as the need for a material transfer agreement." does not necessarily mean releasing the source code but just the binary or a web-application created from the code. Where did you make the assumption that they should give their source code to you? The word "tool" refers to full apps and not original uncompiled source code.
Contacting the managing editor for the publication to explain the
situation....
And what do you think the editor would do? Punish the authors because a random stranger on the internet tells him something bad about them? You can rest assure, this action will have little effect on the authors and only reflect bad on you.
Contacting any granting agencies who have provided...
Why do you assume that under the rules of their funding agency they should release everything as open source? I have worked in many research projects in Europe and I have never heard of such a strict rule. Perhaps there are some projects or agencies demanding that but I do not think it is the norm as you suggest it is. In many projects, participants are commercial companies and they are usually not interested in sharing their work with anyone else (except the project partners and only during the project's duration). Enforcing such a rule would make all commercial companies to not want to participate and that is against the policy of funding agencies.
Have you ever stopped to consider that the PI perhaps relocated and did not get those emails? Are you 100% sure that the authors did not reply your emails on purpose? And even if they do, are you sure that they broke some rule as you assume they did? In your shoes, I would not be too sure. And starting a full-scale war, will do more harm to you than them.
Also if you want something, be nice. Sometimes it does not work. OK. Bullying people into doing what you want is not an efficient long-term policy.