While I completely agree with you and have had the same experience, I'll try to phrase it in a way that might "click" for you:
1. An account is an abstract bucket that aggregates things of the same type. For example, the "Sales" account contains all the income from sales and the "Furniture" account represents the value of all the furniture. The "bank account" represents your dollars stored in the bank.
2. A transaction is an event where something of value is moved from one account to another. For example, when you buy furniture, money goes out of your bank account and is "transformed" into furniture. When you get paid, dollars go from an "Income" account to a "Bank account".
3. The goal of double-entry bookkeeping is to show both the source and destination of every transaction. For example, if you have furniture worth $375 in your possession, where did that value come from? Right, a transaction "debited" the furniture account by $375 and also "credited" the "bank account" with the same amount.
I suspect the original article only makes sense if you already have a solid understanding of both graphs and double-entry bookkeeping though...