Looks like you found relevant commit causing this issue for me. I agree that adding similar conditions to doc/python_api/sphinx_doc_gen.py should help.
Sep 5 2020
I'm using same version of Blender to generate the docs. I'm building blender and using it to generate docs. Yes, I might have configuration which has disabled hair and pointcloud stuff, but this configuration is same as one used for 2.83.5 and earlier blender versions. All enabled stuff and some disabled stuff should be listed in first message. What is required to enable hair and pointcloud? Did requirements change from 2.83.5? And are they different in master branch and commit a96283ba511d7ebf2c2ec2db16815b5a4b2979df ?
Sep 4 2020
Ok, I ran some tests. When I'm using commit a96283ba511d7ebf2c2ec2db16815b5a4b2979df (branch master), documentation builds fine. When I'm using branch blender-v2.90-release (either from tag v2.90.0 from git, commit 0330d1af29c067cf309e4798f5259e01a8c3c668, which is also at the moment the latest commit in that branch,, or from tarball https://download.blender.org/source/blender-2.90.0.tar.xz) I'm getting error described in first message.
I'll try checking later if source from commit you mentioned builds fine for me.
I'm using sources from https://download.blender.org/source/blender-2.90.0.tar.xz. With https://download.blender.org/source/blender-2.83.5.tar.xz there were no such issues for me.