I recently edited a tutorial on this forum about the MATE Dock Applet. It was written by someone who likely didn't have a firm grasp on the English language (non-native speaker I suppose?), and I edited it for brevity (believe it or not) and syntax. It's still not perfect, but it's a lot more readable than before: Alternative dock with win hotkeys.
The pertinent part of that document is:
In other words, I guess you shouldn't right-click on the application icon, but rather hover over it and click "Pin to Panel" in the menu that pops up just by hovering over the icon. Try that and see if it works.