Gratitude involves recognizing a blessing, acknowledging it as a gift from Allah, and showing thanks in words and conduct. Eating is ordinary; gratitude gives this ordinary act an important moral quality.
For example, two people receive a similar meal. One appreciates it, avoids waste, and thanks Allah. The other complains needlessly and wastes it. Their physical act is similar, but their attitude toward the blessing differs.
In الطَّاعِمُ الشَّاكِرُ, الشَّاكِرُ describes الطَّاعِمُ: “the eater who is grateful.” Keeping the descriptive word is necessary for an accurate meaning.