The issue here is that the Homecoming logo is hosted in an embedded IE/Edge browser control. It ignores the default browser because, under the hood, it's already showing in IE and thus past the point of deciding which browser to use.
The solution would be to handle the OnNavigate event of the embedded control by cancelling it and launching a new process to get the Operating System to deal with the URL, which it will do by opening it in your default browser. Tequila already has code for launching a new process, to launch the game, so in theory it would be pretty straightforward. I've only had sight of what seems to be an old version of the source, on my phone, so don't hold me to that. :)
Edit : I've just had a proper look at the Tequila source code. NewWindow is the event that needs to be handled but its and it's more complicated than I thought because of issues with the way that this event had been implemented in the .NET framework. (The URL is not easily available.)