1. Draw a cat the way I told you.
the way 是 in the way 的省略说法。不可能作宾语,draw 的宾语是 a cat。现代英语中,the way 可以独立用作连词,相当于 as,引导方式状语从句。
Draw a cat the way I told you. = Draw a cat as I told you. =Draw a cat in the way (that/inwhich)I told you.(这种表达很少见了)
2. The thing is as simple as I think.
简单理解:这是比较结构。第二个 as 指代前文整个句子的内容(不是结构),同时作 think 的宾语。