I would say: It means the three main elections, namely those of the 1500-members Election Committee, of the LEGCO and of the chief executive, will all be held following new rules. I'm not sure where you would use "are" in this sentence...

"That" stands for "the (main) election": the three main elections, namely – the election of the 1500-members Election Committee, – the election of the LEGCO, – and the election of the chief executive, will all be held following new rules. You can't use "are" (or any other verb) there, how should that work?