No, it's not an attempt to simplify. Advanced textbooks define it in the same way.

Do you have a source? I've only ever seen it defined the traditional way. Besides, you can increase the money supply and not get inflation (defined the usual way). Inflation happens when the money supply increases more than the economy needs.

Inflation happens when money supply increases more than the value of the goods that you can purchase with that money supply. It isn't about needs, but things that can be bought, especially those with limited supplies like housing.

So if money supply stayed the same but a crisis reduced the supply of goods, while demand increased, then those raising prices are ... not inflation?

Say Price = Money supply / value of goods

If price goes up then inflation, if price goes down then deflation. If value of good goes down and money supply stays the same, inflation.