BrowserType does not matter, but mine is set to 2. Did it start downloading an update for the launcher, or were you able to login and start downloading the game itself? Based on a quick Google search some Windows users are getting that error too, so it may not be Wine-specific. Trying again enough times might fix it. Some users also report getting around it by using a VPN. One basic thing to check is that you have enough space on the filesystem where the game is installed.

Are you running the standalone or Steam version of the game? Did you copy it from a previous installation or do a fresh install in a new wineprefix?