The MaLBI”M comments on the end of this verse, as follows:
Though the mitzvah is the candle that lights the path in a person’s life, if a person does not walk on “the path of life”, the light of the candle will not be beneficial at all. That which leads a person on “the path of life” is the intellectual moral rebuke, for by accepting this rebuke, and fear HaShem, he will walk on “the path of life”. By accepting this rebuke and fear of HaShem, he will benefit from the candle of the mitzvah and the light of the Torah to guard him from the “snares” and the “thorns” on the “path of life”, as is written, “Fear of HaShem is the beginning of knowledge…”” (Mishlei: 1; 7)
Perhaps the GR”A is comparing a fast from food to the light of a candle which signifies a mitzvah and compares the bridling of his mouth and of his [negative] desires to “the rebukes of musar (moral rebuke)” which is comparable to “the path of life” which refers to the life that one leads by walking in the way of the Torah. Hence, while a “mitzvah”, such as a fast from food, is very important, and is the “candle” which lights up “the path of life”, the “candle” – “fast from food” is useless if one is not leading a life of Torah by traveling down the “path of life”. Becoming positively affected through moral rebuke and fear of HaShem, can be accomplished through a “fast from speech” and bridling of negative desires. Thus, a fast from speech and bridling of one’s negative desires can benefit the individual far more than a physical fast from food and self-affliction.
 [Chofetz Chaim’s note: “I have seen a similar [teaching] in sefer “Rosh HaGivah” (pg. 8b, words beginning “Shema bini”), [where we learn as follows], “When a person wants to accept a fast upon himself as a free-will offering, it is preferable to accept upon himself a “fast” from speech, than to accept upon himself [a fast] from eating. For, [as a result of this “fast” from speech], he will not be harmed, [both] in his body [and] in his soul, and he will not become weakened through this “fast” [from speech].”]