Having read the web page before posting that is not at all how it reads to me, nor It seems to the OP.
It reads pretty clearly to me as that if your carry on exceeds either the required dimensions or the allowed 7kg weight for DUB to LBA (and you are caught) it will be taken off you and gate checked. If that occurs you will be charged the £35/35 Euro, whatever class you are in. I can understand them having a sizer at the gate, but scales?
Maybe the agent will be lenient and waive the charge, especially if you are nice to them and accept it without a debate.
The OP hasn't stated whether her carry on exceeds weight or size. If happy to.run the chance of being checked and stopped then the answer to the question asked is that you can pretty clearly (from the rules on the website) gate check it. But you may well have to pay to do so.
Presumably this charge is to try to stop people playing the system.