I'm a bit familiar with law (took 2 courses at uni) and understand how awkward the language can be.
For instance, maybe Mozilla has to say "you grant us the license" instead of "you grant Firefox the license" because licenses can only be granted to legal entities, and Firefox is merely a software.
And it's also true that you don't navigate the internet directly; you use the UI of Firefox to enter your data, and then Firefox uses it to send requests to the server. It acts on your behalf, exactly as the text says.
Those were my initial thoughts based on my limited knowledge about law. It might very well be wrong.
But the problem is indeed what a lawyer could do with this, and I'm sure it grants Mozilla more rights than necessary. I also find it suspicious that none of this was an issue for over 20 years, so why would it be now?
@volpeon@icy.wyvern.rip