Thanks Bob,
OK, I went deep into the server using PhpMyAdmin and found the templates. Just for good measure I copied the code for the templates from the PhpMyAdmin page and saved them to my desktop.
There are a couple of differences between the two Articles templates that are listed in the REVO MODx Manager and the rest of the site templates that do not show in the REVO Manager. An image might be easier to show this: please make sure you open your browser window wide enough to see the full chart with the properties column showing.
The main difference I see is with properties.
AFAIK, the site owner has not done anything specifically that would prevent the templates from showing in the Manager. For now it might be that I have to edit the templates from inside PhpMyAdmin instead of the MODx Manager. But I would like to fix this. I am also mulling over if I should convert the entire site over to ProcessWire (a system that I am playing with currently)...