There is no client to download yet. The download page says the same thing, and will carry the real builds, their sizes and their checksums when there are any.
Why a separate app at all
The site is the site. A world that people walk around in wants a window of its own, consistent performance, and access to the machine it is running on in ways a browser tab is deliberately not given.
Both comparable platforms made the same split: a website, and a native client for the worlds. Neither runs the game in a browser.
What stays on the site
Accounts, the catalog, the figure, the forums, settings, messages. A conversation started on the site is meant to continue in the client, because it is one system with two front ends rather than two systems.
What you will be able to check
Every build will be listed with its version, its size and a SHA-256 checksum, so you can verify that what you downloaded is what we published. The download page explains how.
When
No date. Saying one would be making it up. The pieces being built now are the ones the client needs to exist at all.