Bullshit
If the Founding Slave Rapists lost... we'd all have to suffer the abject horror of being.... Canadians!!!
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Seriously, that's what would have happened. Briitsh North America would have become something like the Dominion of Canada.
Now, of course, none of us would exist in that timeline, because the exact circumstances of our parents meeting much less copulating on a certain day would be unlikely.
The UK was a parlimentary democracy. If anything, on the alternate timeline, slavery would have ended a lot earlier than it did, without a civil war. (The British Empire abolished slavery in 1834)
Now, that would be for the US EAST of the Mississippi. Would the UK have taken Louisiana from France after the end of the Napoleonic Wars? Probably. Would they have done a mad territorial grab against Mexico? Probably not.
Here's the thing, Canada has a pretty good system. They have universal health care. They have elections where someone doesn't get elected after the people say no, loudly to him.