I am confused at the explanation below which explains why nominal GDP must be deflated to get real GDP. I thought the GDP deflator would decrease if prices are declining, so how does this result in nominal GDP being "deflated"?
The GDP deflator is, by definition, the price of real GDP. $$ GDP(nominal) = Price \times GDP(real) $$ It is an index that is equal to 1 (or sometimes quoted as 100) in the base year. That means in particular that nominal GDP is the same as real GDP in the base year.
Deflating nominal GDP means removing the price (or nominal) effect from GDP, leaving you with GDP in volumes (or real GDP). More specifically, nominal GDP is divided by the price index.
Unlike the text in green suggests, this independent of how exactly prices have been moving. To get real GDP, nominal GDP always needs to be deflated. It's a technical term. And there is really not much you can say about real GDP by just looking at prices. Irrespective of how prices move, real GDP can be growing or falling. To be able to say anything, you would need also information about either nominal or real GDP. In other words, you can solve the equation above for real or nominal GDP only if, in addition to prices, you have info about the other.