Basics Combat would remaing largely the same, but the "grid" would now be represented by the 16x16 tiles you see here. A few modifications would have to be made for the system to fit the new grid and remain sane.
Initiative and statsI still haven't figured out how to do initiative right in this game. In the Homestuck RPG, combat stops every time one player needs to take there turn and runs through the enemies in initiative order until it hits another player. That would be a lot of breaks for an already-slow RTD, though, so I give the characters far down on the initiative list a slight bit of tactical AI in addition to the actions they took. Whatever. 1d20/player, highest goes first.
Re: stats, nothing except for move would function differently. Strength bonus, dexterity bonus and such are all added to any appropriate roll. You die when HP runs out and can't cast some spells when MP runs out.
Movement"Move 3", the base Move stat for most characters, means you can walk up to three tiles in any direction. If you can move up or down (like Bradley), this applies to all eight directions (even diagonal). You cannot move through enemies, but you can move through allies.
Grounded characters can move over 1-tile-high spaces for no extra move cost. This is because it counts as a single diagonal move, and diagonal movement costs the same as any other movement in this system.
JumpingThe only new mechanic. To bypass enemies and obstacles during combat, characters can JUMP over them instead of moving forward. Each tile moved diagonally or upwards during a jump counts as 1 move. Unlike flying characters, grounded characters will fall to the ground at the end of their jump, so be careful that they're not above a hazard, drop or enemy that might harm them!
Range and Area of EffectThe same with a few tweaks. An attack with range 6 can target anything up to six spaces away in any direction from you. However, larger targets (like Humans) can take up two tile or more, which means that attacks can be started (and targeted) at more than one tile.
Area of Effect remains the same. An attack that targets a "3x3 square" will do that, spreading out in a 3x3 square from the target tile.