How is this ambiguous?
1. you must have your license on you
2. must display it to LEO/other persons on demand WHEN AND IF REQUIRED BY LAW TO DO SO
The problem is that you have to go way out of your way to make the second half of the highlighted sentence mean anything at all. There are two possible interpretations:
Simple reading interpretation:
When read as simply as possible (which is how laws are supposed to be written and read) there is no requirement to ever display your license to anyone. It says that you shall DISPLAY the license "...when and if required by law to do so". Okay, so which law requires you to DISPLAY the license? There are plenty of laws that require you to HAVE the license, but there is absolutely NO other law that I know of that requires you to display your license. This is the only one that mentions displaying it, but this one doesn't actually require you to do so. So the entire thing is an endless self-referential circle that doesn't ever go anywhere, and so you don't have to display your license ever.
Complex reading interpretation:
The only way to interpret this law to say that you ever have to display your license is if you assume that "...when and if required by law to do so." is in reference to the first half of the sentence "...have his or her concealed pistol license in his or her immediate possession..." and not in reference to what immediately proceeds it "...shall display the same upon demand to any police officer or to any other person...". However, that is not how English normally works, so we are basically pulling that interpretation out of our backsides in order to avoid the second half of the sentence having no purpose at all.
As Right Wing Wacko said, it is a "...poorly worded piece of law...". We know what was intended, but that is NOT what was written at all, and we have to do language contortions to interpret it to say what it was meant to say.