Well to start, you're gonna need an alternate American Revolution to account for the Canadians holding onto Delaware. Maybe get the rebels to form a South-dominated expansionist republic which rolls west without regard for Native treaties or European borders, even buying Rupert's Land somehow. Then you'll have to get an alternate Opening of Japan, possibly resulting in the isles becoming a sort of British protectorate. After that, perhaps some kind of civil war happens that leaves one particular faction with the Crown's holdings in the New World and the Far East.
Great idea! I actually brainstormed about 7 scenarios (in brief) but didn't want to spam the thread about it. However, since a scenario has already been presented (and one which mostly aligns with one of mine), I figured I'd share my thoughts:
1. The Dutch colonize more of North America, leading to permanent settlements there. Then they open up trade with Japan and turn it into a part of their colonial empire.
2. The Portuguese land in North America initially rather than South America, establishing colonies there. They open up trade with Japan and turn it into a part of their colonial empire.
3. Somehow the Japanese discover the Americas first and manage to keep it secret from the rest of the world. They establish colonies in Central America then island-hop to that part of North America which they colonize.
4. Some other power (maybe the Norse via Vinland? Or someone else entirely?) discovers North America, colonizes that part, then moves on to colonize Japan (and other parts of East Asia).
5. The British decisively win the War of 1812, drawing part of the nascent US away into British North America. Somehow a civil war develops in British North America, leading the former US territories, Quebec, part of Ontario, and the Maritimes to break away from the rest of British North America. Somehow later, this new country forms a federation with an expanded Japan (or colonizes it), leading to this monstrosity.
6. Somehow the Americans win the War of 1812 very decisively, taking control of all British North American territory. A civil war breaks out in which the abolitionist North breaks away in, say, the 1830s or 40s. Then this breakaway nation establishes relations (either cordial or colonial) with Japan, leading to this abomination somewhere down the line.
7. Quebec and the Maritimes join the American Revolution while the South either doesn't or breaks away after a time. This different US then opens up relations with Japan, leading to map in question.