For FOBTs that you would find in a betting shop, yes, they all require connectivity. But - the machines are not on the public internet. They sit on a LAN in the shop, and talk to a back-office PC (as do the cashier terminals) which are connected via VPN to the platform operator. Most machines are wired for ease of connection and maximum reliability.
Depending on the platform, game updates are pushed in packages to each shop overnight, or download in the background.
Bandwidth wise, most shops have a standard BT ADSL line, some remote shops (highlands and islands) have as little as 256k download speed. This is slow but sufficient to download a new game package once a month or so, and upload fault logs etc as necessary.