Call her Bonde. James Irene Bonde.
Okay, I laughed. Certainly, we could have seen a James Bond figure entering the scene coming, given that Mycroft is involved in the creation or streamlining of some sort of intelligence unit, for which Albert has been recruited – it's not much of a leap to guess that that unit is actually MI6. It also seemed unlikely that Irene Adler would follow her canon trajectory of marrying a Mr. Norton and gracefully exiting the scene. But still – Irene Adler as James Bond(e)? That's more The Bleak Old Shop of Stuff territory than anything related to canonical Holmes.
That said, it is difficult to fault the Moriarty brothers for bringing Irene into the fold. She's certainly an accomplished actress and schemer, and she has gained Sherlock Holmes' respect and/or affection, something that could prove useful going forward. More importantly, as one of Holmes' best-known rivals, she's not a character one just brings in only to jettison once the storyline is over. The fact that Sherlock very clearly knows that rumors of her death have been greatly exaggerated may also appeal to William Moriarty; he's not likely to assume that Sherlock will just buy her death as-is, and that means that he could potentially use the other man's feelings – and love of fair play – to his own advantage.
Because Sherlock burning the note containing the name “Mr. James Moriarty” is almost certainly a declaration of his intent to play this one as it lies. Sherlock Holmes has no interest in the easy answers the game thought up by William would have provided, something our Lord of Crime presumably understood about him. When he burns the note with a smile, he's not only saying he'll find the answers himself, he's also announcing that he doesn't believe Irene to be dead – and that he trusts the Lord of Crime to keep his word on that front. There are rules, apparently, and even if Holmes and Moriarty aren't following the same ones, they do plan on following them to the letter.
Essentially, the entire “A Scandal in Britannia” story arc was setting up the next phase of the Lord of Crime's plans. Up to this point, they've been working small – a villain here, a monster there. With Albert's working relationship with Mycroft Holmes now on the table, however, they have the means to make much bolder statements, which is why it's so important that Mycroft be manipulated into looking the other way. I'm not one hundred percent sure that William knew that the man history knows as Maximilien Robespierre was really Sherrinford Holmes, but he had to know that there was more than a matter of historic preservation behind Mycroft's interest in the papers proving that the French Revolution of 1789 was planned by the British. By forcing him to say out loud who “Robespierre” was, he tightens the noose around Mycroft, ensuring that the British government will look the other way as the Lord of Crime carries out their equalizing schemes. (That whirring you hear? That would be Robespierre spinning in his grave.) Now if they can just work in a Charlotte Corday metaphor somewhere, I'll be truly impressed.
Despite the bizarreness of some of the plot points in this arc, it does do an interesting job of setting up Mycroft Holmes as both a decent take on the canonical version and someone who has the power to ignore whatever Moriarty is getting up to under his nose. Sir Arthur Conan Doyle never specifies what Mycroft does, exactly; in His Last Bow (1917) it is said “The conclusions of every department are passed to him, and he is the central exchange, the clearinghouse, which makes out the balance. All other men are specialists, but his specialism is omniscience... only Mycroft can focus them all, and say offhand how each factor would affect the other. They began by using him as a short-cut, a convenience; now he has made himself an essential.” Although this slightly contradicts the description of him given in The Adventure of the Greek Interpreter (1893) – “…he has no ambition and no energy. He will not even go out of his way to verify his own solutions, and would rather be considered wrong than take the trouble to prove himself right.” – we can see both pieces of Conan Doyle's often contradictory character development in play in Moriarty the Patriot's take on the character. He'll let the Lord of Crime carry out their plan both because to do so will aid in his vaunted omniscience – and it's easier than trying to stop them.
For now, at least.
Moriarty the Patriot is currently streaming on Funimation.