No, you don't need to change.
It says "to find records". RecordID is always there (not depend on table definition), so API use it.
Be aware that the RecordID is not persistent. It can and will change if you import records from one copy of a database to another. Therefore, it should not be relied upon as a relational key.
You can use RecordID as part of PHP scripting to locate a record assuming you fetch it from one page, then use it in the next. But don't assume it will always stay put.
You can also configure some PHP calls to use your serial number, if you like, but many of the API functions rely on RecordID.