Having issues when adding Vcenter

The docs mention this only briefly in the text, but do not show it in the screenshot.

[…] and set the condition to the appropriate host as defined in Checkmk

In your “VMWare ESX via vSphere” ruleset entry, scroll all the way down to “Conditions”, activate “Explicit hosts” and select your vCenter host so this rule will not apply to other, non-vCenter hosts.
(Of course you can also use different conditions like tags, labels, folder, … whatever suits your environment)