Eating in Order to Bentch

The Sefas Emes zy”a understands the pasuk to mean that after one eats and is satisfied, he naturally comes to bless Hashem. The Gemara (Brachos 35A) says that it is a “svara” (logical conclusion) that one may not derive enjoyment from this world without making a bracha. Thus, it is natural that one automatically blesses Hashem after eating.

He adds that eating provides a person with a spiritual arousal to bless Hashem. Thus, the pasuk is saying that after one eats, he is aroused to bless Hashem.