Yes, here is a fuller explanation:
The Monero GUI has a Shared RingDB. This means that when you spend one of your outputs using the Monero GUI, a record will be kept of the ring members that were used for that transaction in the Shared RingDB.
The "Shared" in Shared RingDB means that this database is shared between all wallets on your computer, regardless of which fork they are transacting on. Therefore if you spend an output using your Monero wallet, then when you spend the output again using the MoneroFork wallet, the same ring will automatically be reused because both wallets are using the same Shared RingDB database.
This records rings used by outputs spent on Monero on a key reusing
chain, so that the same ring may be reused to avoid privacy issues.
This section is necessary in case the wallet that you used on the other Monero fork does not support Shared RingDB functionality. This section therefore lets you manually record a ring into your Shared RingDB, because it would not have happened automatically.
It is necessary for untraceability reasons to use the same rings on every Monero fork when spending an output that exists on multiple forks.