All the data on Steem-Engine are recorded on the Steem blockchain. To the nodes (servers) that run the Steem blockchain that data/transactions are just user-defined random data that nothing is done in response to. Steem-Engine transactions are processed by servers (currently only one) that are a completely separate set of servers from the Steem blockchain nodes.
I hope that cleared it up for you. The main thing is that a copy of the record of everyone's Steem-Engine tokens will exist on the new chain. It's up to the Steem-Engine team to update their nodes to use the new chain.