There are several other extensions in the Chrome Web Store which do translation and definitions. The mechanism the extension uses to show translations determines whether it will work in Chrome's PDF viewer. Extensions which add an option to the right-click menu will work in the Chrome PDF viewer, while the extension you mentioned just depends on clicking on the word, which does not work. A couple that I tried (just from a quick search):

Both of these worked fine in the built-in PDF viewer, as shown above. If your PDFs are opening in an Acrobat plugin, you'll want to disable that so that you can use the built-in one. You can do this by going to chrome://plugins and clicking Disable next to Adobe Acrobat. Make sure that Chrome PDF Viewer is enabled.