Snap just needs to have the Chrome Browser installed—for the most part, it can run on any laptop that can install the Chrome Browser. It can also run on a Chromebook, which are generally lower powered machines, so your computer need not be a powerful computer.
We've encountered many issues with the native desktop version of Snap, so we've discontinued support for it, as we're trying to move towards being cross-platform with the Chrome app so we can maintain one version.
For the Chrome app, you only need to be connected online for the initial installation. Once the Chrome app is installed, you don't need to be online to use it.