The traditional accounting identity is something like "Assets = Liabilities + Equity", or in an expanded form "Assets = Liabilities + Contributed Capital + Revenue - Expenses - Dividends" (from Wikipedia https://en.wikipedia.org/wiki/Accounting_equation). You can re-arrange that as:

Assets + Expenses + Dividends = Liabilities + Contributed Capital + Revenue

Traditional accounting takes this as says: "All accounts have positive values. All transactions contain an equal number of debits and credits. Debits always come first, are always written on the left, and so it (sort of) makes sense for debits of left hand side accounts to always increase the value of the account, while debits of right hand side accounts always decrease the value in the account. Similarly, credits come second, are always written on the right, credits of right hand side accounts increase the value of the account, and credits of left hand side accounts decrease the value of the accounts."

It turns out if you work through the implications of this, it works perfectly. I buy lunch for $5, so I must have a $5 debit and a $5 credit. That's an expense; my expenses are going up, expenses are on the left, so they go up via a debit. The matching credit could be to cash; cash is an asset, it's also on the left, credits make left hand accounts go down, that makes sense. Or the matching credit could be an accounts payable account, that's on the right hand side, and credits make right hand accounts go up, which again makes sense.

The core logic here is that changes must balance. If your changes are both on one side, one will be positive and one will be negative (summing to 0). If your changes are on opposite sides, either both will be positive or both will be negative (still summing to zero).

But, you could also re-arrange the equation further:

Liabilities + Contributed Capital + Revenue - Assets - Expenses - Dividends = 0

Algebraically, that's the same. If you built a system on that, you could say something like "All transactions must sum to zero. Asset, expense, and dividend accounts are subtracted from the balance, while other accounts are added to it." That still works. My $5 lunch increases expenses, which is a "negative type" account, so I have to either increase a matching "positive type" account (like liabilities) or decrease a matching "negative type" account (like assets) so everything stays zero. It doesn't feel...easier, but it works.

Or you could take it a step further, and weirder, and say:

Assets + Expenses + Dividends + Liabilities + Contributed Capital + Revenue = 0

That...uh....doesn't work mathematically, unless you flip the sign of all assets, expenses, and liabilities. So maybe:

(-Assets) + (-Expenses) + (-Dividends) + Liabilities + Contributed Capital + Revenue = 0

I dunno, this is getting a bit weird. Now my $5 lunch is a $5 credit and a $5 debit. Expenses has gone up, so that must be what the author calls a credit, but since expenses is a magic negative account the displayed value will go down. And then we must have a match debit (in the authors terms) which will make an account go down. And again, we can pick assets to go down (if I spent cash), except again assets is a magic flipped account so will make the displayed value of assets increase, or we could pick liabilities which is a normal account and thus the value will actually go down.

Technically, all this is interchangeable. However: The standard form (LHS = RHS, debits increase LHS and decrease RHS, credits increase RHS and decrease LHS, debits = credits) is universally used around the globe, and has been in active use since the middle ages. It's also, in my view, relatively intuitive once explained. The middle form (all accounts sum to zero) is unorthodox, but also fine. Both require to to know an equality, and ensure that each transaction respects the equality.

The linked form is, in my view, by far the least intuitive, and also re-uses accounting terms with a different meaning. Not only does it not, in my view, help novices understand accounting, but I fear learning it makes it actively harder because you'll need to unlearn it first.

But it does, technically, work.