Strategy games usually send input, while shooters usually send gamedata. However there are exceptions. For example Halo : Reach runs in lockstep in some online game modes, sending only input.
There are multiple reasons for this:
- Shooters have a lot less game data than strategy games
- It's easier to keep the game in sync
- It reduces lag as long as the game data to send is small
Shooters have a lot less game data than strategy games
A typical shooter has 10 people shooting at each other. The data for this is small, for each player you only need to know the position, direction, speed, health and current weapon. Once people start shooting it's going to be a bit more but that data doesn't need to be retransmitted to every player. In strategy games you have to send this for all 100 units of all the 10 players, which quickly explodes into a gigantic game state.
It's easier to keep the game in sync
When everyone sends their game data the server knows exactly the state of each player's game and can thus easily compare everyone's game state to see if it's in sync. If it isn't in sync the server can usually tell who isn't, because the data is received from multiple sources, and can send messages to correct it. If the server only receives input and through some weird errors one player goes out of sync then there is no easy way to repair it so the player has to be dropped.
It reduces lag as long as the game data to send is small
When sending input data you are usually running in lockstep. This means that each client get's a turn, the server then decides the outcome and sends the changes (as input) to all the clients. This means that you have to keep waiting on the player with the highest latency. (You could run without lockstep, but I have no idea how that would work on just input since you're bound to desync soon then).
Why don't all non-RTS games just send game state
There are also a few good reasons for just sending input data. You can't cheat with input data, while it's fairly easy to cheat with modifying your game state, and it's easier to resolve bug with happen due to lag since everyone is running at the pace of the slowest player so everyone sees the same thing happening for each event.