According to the info page, "While a persistent connection is not required, Xbox One is designed to verify if system, application or game updates are needed and to see if you have acquired new games, or resold, traded in, or given your game to a friend. Games that are designed to take advantage of the cloud may require a connection."
The gamer may use their mobile device: "In areas where an Ethernet connection is not available, you can connect using mobile broadband." The rate required to connect once is considered low by global standard (1.5Mbps).
Microsoft had previously stated that gamers with no internet at all would have an exemption. It remains to be seen if this is the case. On the plus side, gamers with a constant internet connection don't require a disc at all to play.
On the other side, there will be no fee for used games, which is probably more important for gamers, since many of them already have an online connection anyway.