Yes, and no :)
I think the article is speaking about the image file size (in bytes), and not the image size itself (in pixels) which is indeed unchanged.
But, to be accurate, one of the tradeoffs of the JPEG algorithm can also reduce an image size. In the compression, the RGB image is split into three sub-images, one which is the luminosity component (more or less a black and white version of the image) and two that represent the color information. These three images are compressed separately.
The JPEG format exploits the much greater sensitivity of our eyes to luminosity than to color, and to do so it will scale down the two color images to half size (2x scale horizontally or vertically) or quarter size (2x scale both horizontally and vertically). This is called "chroma sub-sampling". This reduces the amount of data to compress: if a sub-image is
1, without sub-sampling you compress
1 + 1 + 1 = 3, with halved chroma you compress
1 + ½ + ½ = 2 and with quartered chroma you compress
1 + ¼ + ¼ = 1.5, which is half the original size. This of course translates directly into the equivalent file size reduction.
This is usually hardly noticeable, and the "high-quality" JPEGs (Q=98) from my middle-of-range camera have their chroma halved.
In image applications, this sub-sampling is either an explicit option, or is bundled with the "quality" (for instance, chroma is halved for Q=70-90, and quartered below Q=70).