How can I stop macOS re-installing default apps and data I've previously deleted when I update the OS?
When removing "parts of the operating system" any update you get through the software update mechanism (AppStore) will re-install these apps and processes. Well, at least partially. Even so called ComboUpdaters were in fact delta updates relying on some previously installed base for many of the components supposedly contained in the ComboUpdater in full. 

This results in a problem for those wishing to customise their installation: after removing parts Apple assumes are present some parts will only look like they are fully re-installed when in fact they are now 'present' but broken. This is what was experienced in the question when supposedly re-installed apps are now greyed out.

That leaves the customiser a couple of options:


Leave the system in an Apple authorised state. This has to be decided on from the start, though. ComboUpdaters are no longer a reliable way to 'repair' such a state back into working condition and most backups from an extremist-customised system will be tainted. A re-installation might be in order to get back into that state.
Download the standalone updaters from Apple, while that's still possible. This is the usage/how-to request in the question. But it is a tough choice: In case of the macOS High Sierra 10.13.1 update that would be here. You might then use a  manual installation of individual parts of the updater package(s). This might be done with a programme like Pacifist. But this process is very time consuming, and error prone, at least. If there are firmware updates or some undocumented non-obvious scripts to be applied in this update this procedure reaches quickly its limits and it might even be almost impossible to replicate what the updater did. Errors will very likely accumulate along the way.
Re-delete or re-disable everything you previously disabled (that means you should prepare at least a script for that). This is clearly the best option if you start updating from a non-Apple approved state of system manipulation. If Chess and iCloud were useless before they are useless now, in their (half or cmpleely) broken state. Note that this answer does not discuss any SIP related issues, since that has be a non issue in the scenario given anyway. This adds just one additional step of after update maintenance.