Notes

1. Mr. He tied at least 3 games.
Because of this, Mr. He could not have played 4.0, 4.5 or 5.0 games.
2.Nate finished 1/2 a point ahead of the player with the last name Fallows.
Because of this, Nate's last name is not Fallows, Nate could not have finished with 3.0 points, and the player with the last name Fallows could not have finished with 5.0 points.
3. Two of both Matthew's and Caleb's games were not wins. Neither one of them was within half a game of Jack.
Because of this, Matthew and Caleb finished with either 3.0, 3.5 or 4.0 games. However, Jack was not within half a game of either of them, which means that Jack either finished with 4.5 or 5.0 points.
4. The player with 4.0 points and Mr. Cheung were both undefeated until the very end, but in their final-round match-up, it was Nate who prevailed.
Because of this, Nate is either Mr. Cheung or the player with 4.0 points. However, since Nate won that final-round game, he would not have finished with only 4.0 points. Therefore, Nate's surname is Cheung, and he finished with 5.0 points.
5. Nate, Jack, and Mrs. Brown all finished, in the above order, with at least 4.0 points.
"In the above order" is an odd detail to include, because the order the puzzle is suggesting is not yet known. What we do know, however, is that Nate finished with 5.0 points, so the following names must follow in descending order. Jack finished with 4.5 points, which means, as per Clue #2, that he has the last name Fallows. Mrs. Brown finished with 4.0 points, and since Roxanne is the only girl on the list, she must have the surname Brown. This means that Matthew and Caleb have the surnames He or Graham and finished with 3.0 and 3.5 points.
6. Unfortunately for the Rogers chess team, Matthew only finished with one win. At least Mr. Graham was good enough to have come away with 3.
Because of this, Matthew's last name is not Graham, it is He. That leaves Caleb's last name to be Graham. Because Matthew finished with at least 3 draws and one win, he could not have had 3.5 points. (1 + 0.5 + 0.5 + 0.5 + 0.5 only equals 3.) Therefore, he finished with 3 points, while Caleb finished with 3.5.