The following line states that you've already installed steam you just need to run the program.
Done steam:i386 is already the newest version (1:18.104.22.168-1ubuntu3)
The following command is simply trying to reinstall it.
sudo apt-get install steam
You can run it via the terminal or if it's easier just type steam in the menu.
Okay well if you didn't attempt to un-install it then you should be able to find it in dash ("Search your computer") it should show up if you type steam.
To run via the terminal, well there are a few ways but for now just open it and type
Then hit enter
In the future when you post code and or terminal output please format it to look like this so it's easier to read :)
[2016-10-02 08:45:13] uninstalled manifest found in /home/hpersniper
[2016-10-02 08:45:26] Installing update...
[2016-10-02 08:45:26] Cleaning up...
[2016-10-02 08:45:26] Update
[2016-10-02 08:45:26] Shutdown Running Steam on
ubuntu 16.04 64-bit STEAM_RUNTIME is enabled automatically [2016-10-02
08:45:35] Startup - updater built Sep 20 2016 18:20:24 SteamUpdateUI:
An X Error occurred X Error of failed request: BadValue (integer parameter out of range for operation)
There are few threads open already that will help you fix any issues you have with setting up steam and or correcting issues just search around a bit! Could you mark this as an accepted answer so that your original question can be marked as solved!