Some little corrections:
a)-thoroughly (in a certain way, just for mnemonic´s sake, -tho_rough_ly.)
b)-Normally the past of of "sit" is "sat" (as a verb), but in the above case Jake and Mattie were seated in front of a bonfire.
What Thomas meant is that one character is in a lower position than the other, and by your further description of the scene Jake is the one.
So, then somebody can safely conclude that Jake is a guy (naturally he is in a higher position, the man is generally taller than the girl and this is the case here.) So, if he grin, he will grin down at her.
Sometimes prepositions used in English gives further 'hints" of a situation (and let the text more concise), examples if you say:
"he ate" (ele comeu), it doesn´t express much, but if you say "He eat up everything there was in the place." this "eat up" means "ele comeu/limpou tudo que tinha, todas as provisões, toda a comida etc.
If you say "I went home" it means "Eu fui pra casa." Whereas if you say, "My home is just up the street." it means, (in a loose translation of mine) "Minha casa é subindo essa rua (significando que "subindo'' é indo na direção sul.)
In the same vein, "I live near the river" may suggest that it´s close but not much, whereas "I live by the river" may suggest that it´s "close by" (it).
These are nuances of English, those prepositions (and other words and resources) turn the communication more natural, concise and helps to add information to the reader.
That said, the "down" add to the information that Jake grinned the fact that he grinned from a higher point (sort of), because he is taller or is in a higher place than Mattie.
Hope it helps.