I've only done a small amount of game programming, but I can't for the life of me imagine why a dead reckoning approach would be necessary or preferable in the first place.

Dead reckoning uses a series of time delta and velocity vector pairs to continuously determine the latest position, right? So in a multiplayer setting, the vector is received over the network and due to unpredictable latency, the time value has to be as well. At that point, why not just send the new position in absolute coordinates? This would avoid any FP arithmetic inaccuracies between devices, especially the kind that accumulate over time as they would by continuously adding vectors on top of each other.

Fighting games derive the game state from a sequence of input states from each player sent over the network. Input states are typically 2 bytes or less (e.g. 4 bits for 9 possible directions on the joystick, 1 bit per button for each of 8 or fewer buttons). Once all input states up to some recent-ish ones for both players are present, the displayed game state is a successor to a guaranteed-correct recent-ish gamestate. Fighting games rely on the notion of sequences of inputs leading to a single correct gamestate because this is apparently necessary to preserve properties like "frame traps." That is, if I use a move and you block it, and I recover faster than you by 3 frames, and then I use a move that comes out in 5 frames, and you also use a move that comes out in 3 frames, I must always hit you and no other outcome must be possible. Some other genres are concerned with preserving other properties, like "if you click on someone's head with a rifle then they get hit," so they quite reasonably take different approaches.

If you can run the same simulation on two different machines using the same sequence of input states from all players and get different results, that's a bug. One way to get this kind of bug is for some parts of the internal state of the game to rely on floating point computations.