Does a desktop pet need the internet?
The honest answer is: mostly no, but not never. Once a buddy is on your Dock, everything you watch them do is happening on your Mac — the 3D model, the walking, the moods, the little stories, all of it drawn locally with nothing fetched and nothing sent. What does need the internet is proving the buddy is yours, and that happens rarely and quietly. Here is exactly where the line falls, because "works offline" is a claim worth being precise about.
What happens entirely on your Mac
The characters themselves. Their models are downloaded once, after you buy them, and then they live on your disk. Everything after that is local: the animation, the physics of their little props, the face that changes with their mood, which activity they pick next, where they wander on the Dock. None of it calls anywhere. Open your laptop on a plane and your buddies carry on exactly as they did on the ground.
What needs a connection
Three things. Signing in, which happens once. Downloading a buddy you have just bought, which happens once per character. And a quiet check every four hours that the account still owns what it says it owns. That check is small, carries nothing about what you were doing, and you will never see it.
Two weeks of grace
If the check cannot reach us — no signal, a hotel network, a week off the grid — the app carries on from what it last knew for up to 14 days. The menu bar quietly says "Offline · last synced" and that is the only difference. Past 14 days without any contact, the buddies pause and their models are removed from the disk; both come straight back with the next successful check. It is the same grace whether you are on a plane, in a tunnel or simply not using the Mac.
Why not fully offline?
Because every buddy is bought, and a purchase that nothing ever checks is a purchase that anyone can copy. Each model is encrypted to your account and your computer, so the file on disk is useless anywhere else. The check-in is the smallest honest version of that: not a login screen every morning, not a phone-home on every launch, just a quiet confirmation a few times a day with two weeks of slack for real life.
What never leaves your Mac, online or off
Anything about what you are doing. If you switch on the feature that lets buddies react to your Mac, it reads the charger, how long you have been away from the keyboard, whether the screen is locked and the time of day — and all of that stays on the machine. Nothing is uploaded, nothing is logged anywhere but your own Mac, and there is no analytics tracking what you or your buddies get up to.
What it costs while it runs
Very little. Two buddies walking the Dock use about 4.8% of one CPU core, they draw more slowly when they are standing about, and they stop drawing altogether when they are hidden or the screen is locked. Being offline does not change any of that — there is no background sync eating battery while you are away.