The Minchas Chinuch (mitzvah 430) writes that the mitzvah of bentching min haTorah is obligatory only when there is "achalta v'savata", a formal halachic act of eating (achila) after which one is satiated. Halacha defines eating as consuming at least a k'zayis of food within the time span of achilas pras (the time it would take to eat a small loaf, which is at most 9 minutes according to some poskim, as little as 2 minutes according to others). Therefore, if one nibbles slowly at a meal, one may not be obligated min haTorah in bentching (MG"A O.C. 210). The Minchas Chinuch extends this chiddush further and wonders if only a k'zayis must be eaten in the timeframe of k'dei achilas pras, or one must eat to the point of satiation during that time frame.
R' Tzvi Pesach Frank (Shu"T Har Tzvi) does not quote the M.C., but clearly disagrees. He cites the words of the Rambam (Brachos 1:1):
מצות עשה מן התורה לברך אחר אכילת מזון, שנאמר "ואכלת, ושבעת--ובירכת את ה' אלוהיך" (דברים ח,י). ואינו חייב מן התורה, אלא אם שבע, שנאמר "ושבעת--ובירכת"
and notes that the only condition the Rambam says which must be met to be Biblically obligated in birchas hamazon is feeling satiated. The Rambam does not say "achal v'sava" -- he just says "sava". (I am not 100% convinced. The Rambam mentions "achilas mazon" at the opening of the halacha and perhaps he is simply adding that satiation is a condition that must be met on top of achila, not that satiation is the only condition that must be met.)
One interesting nafka minah between these views is the famous chakira of R' Akiva Eiger (O.C. 186) regarding a boy who has a big meal just before the night of his bar mitzvah and bentches. When the sun sets the boy instantly becomes bar mitzvah and now counts as a gadol. Must this boy now bentch again because of his experience of satiation as a gadol, or is his bentching as a katan sufficient to exempt from the mitzvah?
Aside from the question of whether the mitzvah performance of a katan counts towards a gadol's obligation, one also needs to factor into the debate the fact that the experience of seviya as a gadol is not accompanied by a formal act of achila done as a gadol. -- whether the seviya of a gadol caused by the achila of a katan is enough to warrant birchas hamazon may depend on whether you take R' Tzvi Pesach Frank or the Minchas Chinuch's position.