Hmm, I get a different error (SPSS v188.8.131.52), even when running SPSS as an administrator, stating:
Cannot install custom dialog to any of the specified locations: and pointing to the TMP environment variable.
Are you able to install other extensions? If the locations as listed in SHOW EXT are blocked, you might try creating the environment variables that extend the places where the dialogs and code can be written.
Go to the Windows environment dialog (win+i and search for environment). Then create two new variables pointing to a known, existing writable location. Mine are set like this.
Restart Statistics if it is running, and it should install.
These installation problems have been pretty much eliminated with V28, which uses a virtual environment for Python (and also installs R with Statistics the way it has done for Python for years).