But what "due process" is isn't universal among all societies because the procedure isn't the same everywhere. Here, if those elements guaranteed to you by the Constitution are omitted - the judge declares that they'll just skip the trial and throw a rope over a tree branch for you - then in the context of our procedures, your right to due process has been violated because the formal procedure has not been followed. Somewhere else, if the method is to have you walk on hot coals, and you don't get to walk on hot coals, then you haven't received due process under that system.
In it's broadest, most general sense, due process implies that there exists some formal procedure for resolving legal disputes (but does not say what that procedure is or should be in a universal way), and that this formal procedure is followed in your particular case. It's procedure versus ad hockery - if they ignore the procedure, whatever it is, then you have not received due process. If it is followed, then you have. But like I said, it only implies that a formal method exists, not what that method should be. Here we have an elaborate and formal procedure, with many elements and layers. Elsewhere, the procedure may not be so formal or so complex. Here, "due process" has a specific meaning that does not apply elsewhere - in many countries, you can forget that idea of not being forced to testify against yourself. That's not a part of the process there, so being forced into testifying against yourself in some other country is not a violation of due process by their standards.
"Due process" just means that the procedure was followed, whatever it is. The fact that the procedure varies so radically from place to place practically guarantees that "due process" doesn't have a universal meaning beyond what I've laid out - that is, until we have a universal method of dispute resolution, anyway.