Actually, using this proposal, it looks like the only way the old chain could survive is if the users that don't want the new chain create a hard fork to reject the blocks created by those that do want the new chain.
Technically this can be done via a standard softfork.
The same is true for any softfork. For example, if some portion of the hashpower were passionately against the OP_CLOCKTIMEVERIFY fork, they could create a competing softfork that makes any block including a OP_CLOCKTIMEVERIFY transaction invalid. If this occurred, then Bitcoin will split into two competing cryptocurrencies (both softforks of the original chain).
If I'm understanding this proposal correctly, it could be described as a hard fork with a simultaneous majority hash power attack on the old fork.
Yes, in the same way a standard softfork uses the majority hash power to attack any chain under the old rules.