In a big change, the Windows 10 Store games can now be played when offline.
It requires some preparation, as detailed in this Microsoft Support post, and is not available for all the game, but it is otherwise a step in the right direction which will makes many gamers’ lives easier. The lack of connection to the Internet will also carry some obvious limitations, like no access to Windows Store or unavailable chat with friends.
Your savegames typically saved to the Cloud will be stored locally and sync at the earliest chance. Similarly switching devices requires previous sync should you want to use the same saved state.
For detailed instructions, answers to frequent questions and additional information it is advised to refer to the Support post linked earlier.