I am getting the error "To create PDF files, you must download the PDF plugin for Hero Lab. This is available as a free download from the updates mechanism."

Yes, I have bought Shadowrun.

I only have the x64 version of HLC installed.

I got the download file for the plugin and installed it. I can find the 4 files you give in the install location of the plugin, but there is no directories for x32 or x64 in either the PDFCanvas directory or the HLC directory.

Okay, we have covered the main possibilities. It may be installing to the wrong location?
Are the PDcanvas files in C:/Program Files (x86)/Hero Lab? (I checked where mine are.)
Otherwise I can only suggest emailing support.

I got it figured out. The problem is that I have HLC installed on my D drive. And no matter which drive I installed the plugin to it did not put the files into the directory on my D drive. I was able to manually copy and paste them and it now works. Alternatively I was just able to "print" the characters and then just select print to PDF and it worked the same.

Yes, default install for HL is C drive. Glad to hear you got it worked out!