Current State of the Game
Factorio is currently in alpha. That said, the game in its current state is extremely well polished and more importantly fun to play. Updates are frequent and the developers are involved with the community and have implemented many suggestions from current players.
Factorio has a very, very active modding community. There are already several huge overhaul mods as well as many mods that simply enhance information availability or make some tasks easier for users. Sometimes these mods are integrated into the core game. The game is not too difficult to mod, especially if you are experienced with LUA, but there are currently very few tutorials to get you started if you have little to no experience.
Yes, there is multiplayer! However, it is peer-to-peer, so there are no dedicated servers: this means that you have to either tell others your IP (currently only works with IPv4, IPv6 support is still in development) so if you aren't able to forward ports, you will need to find someone who can to host. Also, don't expect to be player with people on different continents - lag is a really big issue and desyncing games are still a hastle. However, once past all of that, multiplayer is extraordinarily fun.
Currently the community is holding its breath in anticipation of the .12 update, which will bring many, many new features as well as optimizations. It is expected some time in July, after which the developers plan to pursue putting the game on Steam.
So far I have sunk ~60 hours into this game after buying it a week ago. The gameplay is incredibly addicting and even without mods there is a huge amount of re-playability. The learning curve is a bit steep but if you keep alt-tabbing to the wiki for recipes and comments on what items are used for, you pick it up quickly. If the trailer interested you, I recommend trying the demo.
Currently the game is priced at €15, but that will probably go up after going up on Steam. I highly recommend this game!