You certainly can't check in with your driver's license.
The problem is, according to those rules you'll find in every hotel room in China, if your brother is actually staying in the hotel, then he should be registering at the front desk. For all anyone knows, your brother's visa has expired (or he's wanted by the police, etc.) and you're helping him out by registering for him. They can kick him out after 10pm or so if he's not registered.
As well, if your brother doesn't register, then he doesn't show up in the PSB computer and it's conceivable this might give him problems down the road, especially if he's in Beijing on transit without visa.
I presume OP’s brother will check in with him as co-guest.
The OP is asking if he will get in trouble specifically because his passport is used to check in and register at two hotels on the same dates. His brother is irrelevant to the question.