Can we not do better than this? This is factually incorrect. I'm sure the author knows better, and just thought readers weren't "smart" enough to be able to understand "English is part of the Germanic language family" or "German and English are related", but instead this is just ... no... I don't think I'm being pedantic by complaining about this... But this is like saying that "Spanish started out as French" or "Romanian started out as Italian"
German refers to the language descended from Old High Franconian. English is descendended from the Anglo-Saxon dialects, the languages of peoples who invaded Britain from the western coast of what is now Denmark and the northeast coast of what is now the Netherlands. And then modified with a whole bunch of old Norse influence from Danish and Norwegian invaders. And then with a whole bunch of Old Norman French influence... etc.
If you look for a _modern_ Germanic language that English is most closely related to it would be the low Germanic languages, low Saxon, Frisian, even Dutch more so than German proper. Low and high refers to altitude -- not class or prestige or anything -- the "high" German languages are those that underwent a softening/changing sound shift which came out of the highlands in southern Germany. English, like Dutch, never underwent that sound shift. Hence we say "School" with a "k" for the sch instead of a soft "sch" like in German.