In war the first source of valuable loot comes from dead comrades, and secondly from dead civilians. Valuable objects such as wristwatches are usually of use to the enemy, therefore they should be taken. Obviously gold was a strategic resource during the war. Civilians in combat areas often carry their total wealth in banknotes, and again it was better for this to be recovered from the dead and used. Thefts by everyone from everyone is common in war zones, and especially from vehicles, even tanks, as they carry all sorts of interesting things.
It was a common grisly practice of American marines fighting in the Pacific, and there is documentation that it happened (see below). The obvious reason would be for the gold's value & the potential money to be gained from trading it during or after the war, however, there may be a symbolic or thematic meaning in it too, the concept of collecting a trophy from those you've conquered. A similar scene takes place in the movie The Thin Red Line which is about the Army mop-up actions some months later after the initial Marine invasion of Guadalcanal in August 1942.
There is some documentation that it took place. Robert Leckie writes in his book, Helmet for my Pillow, that there was one Marine who did go around taking the gold teeth out of dead Japanese soldiers' mouths. He kept them in a bag around his neck. He never really explains why the man did it, but as stated above, it would have been worth a lot of money. Many of the Marines fighting in the Pacific wanted "trophies" and yes, gold teeth were just another trophy.
(In the book, he refers to another Marine doing this, but not Snafu. Several smaller characters were amalgamated into Snafu for the purposes of the series.)
However, Marine practices such as this were in response to initial Marine encounters with Japanese atrocities committed against captured Marines. Marines were often tortured, mutilated, and dismembered by Japanese soldiers upon capture, and some strung up alive for bayonet practice. As a result, Marines showed no mercy as none was shown to them.