The way it works is the engine is using the Steam match making system and Steam client to client networking framework. This means you can share levels with anyone that has FPSC Reloaded on Steam. When you join the hosts lobby you will download the map and all the assets required to run the level. You will then be able to play with them. When you are done the levels and assets will most likely be deleted.
You are right in thinking you must have both Steam and FPSCR.
Eventually the system will change so when you build the game in its final form you will be able to define a Steam AppID allowing you to release your own Steam game that does not require the user to own FPSCR only your game. This is not going to be done for a while until the engine is more feature complete.
The system is not fully completed yet but the lobby system works, the map downloading works and you can play together with up to 4 players at the moment.
There is a possibility of dedicated servers as I believe the Steam framework does allow for that but again not for a while, one job at a time.
As a side note if you want to publish your game on Steam and use the MP system that is free you just have to go through Greenlight to get your API details to be able to publish.
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