https://help.yoyogames.com/hc/en-us/articles/230330328-GameMaker-Studio-2-FAQ

Does GameMaker Studio 2 require an internet connection?

When you first install GameMaker Studio 2 you will be required to have an internet connection to
log into the product and download any additional runtimes. After that you can use the product offline,
although you will be required to connect again every few weeks to verify the account using the product.
Note, though, that by not being connected you will not be able to access various features like Account
Management or the Marketplace, nor will you receive any updates to the IDE or the runtimes.

最初の起動にランタイム更新のために接続が必要だね。その後は基本オフラインで作業できる。
ただ、数週間おきにチェックのためにやっぱり接続が必要。