I would suspect that the web page is out of date. Try this:
Click the "Installation Details" button in the bottom left corner of the window that pops up.
Scroll down the list and look for the Papyrus components. I have
Papyrus base elements for code generation (Incubation) 126.96.36.199704200015 org.eclipse.papyrus.designer.languages.common.feature.feature.group Eclipse Modeling Project
Papyrus C++ profile, view and code generation (Incubation) 188.8.131.52704200015 org.eclipse.papyrus.designer.languages.cpp.feature.feature.group Eclipse Modeling Project
Papyrus Designer Unified component model (Incubation) 0.7.5.201704200015 org.eclipse.papyrus.designer.ucm.feature.feature.group Eclipse Modeling Project
I do have a nightly update installed on top of Papyrus 2.0.3 to overcome a couple of issues so your version numbers may be different but I don't recall having to install anything extra to have C++ code generation work.
I updated the wiki page, thanks for pointing this out.
If C++ is not in the list of "install Papyrus additional components", then you are likely already using the Eclipse oxygen release of Papyrus for which C++ code generation is currently not available (or a pre-neon version). An oxygen version will be available with the next release (that should come at the end of this month).