Old Xbox game update

Solution 1:

The Xbox 360 version of Black Ops III doesn't contain local play. It is only the online multiplayer component of the game. Connect to the internet and the game should start.

Solution 2:

first I would address the major question of do you have a hard drive in the system.

An update typically will require some sort of storage either internal or external with a USB drive. second it is possible to install updates using a USB drive by downloading the update from the Microsoft/Xbox site.

Some games may have the necessary update parts on the disk itself but requires space to install it. some systems will try to install updates but cannot get past a certain point due to not having storage.

Finally, you may want to look into the console version as if you are running an older version there are many people that will pay good money for your system if it is not updated as updates have disabled many mods and jtags and finding suitable consoles is getting harder. So you may consider selling that box and get more than enough for another.