It's a core principle of TM law that similar, not just identical trademarks will infringe a registration. "Soundalike" searches are also standard practice before adopting a brand. Amazon is lawyered-up and would certainly have adopted this mark knowing about FyreTV's existence.
The TM rights are pretty directly accessible... they have registrations for the logo[0], the domain name version[2], and the word on its own[3]. If the rights are well-maintained and still active (they seem to be), then the case should not be complicated for FyreTV to win.
No doubt Amazon took the view that the brand tie-in with Kindle Fire was worth the cost of the inevitable settlement. Also, in the battle of Amazon vs instant access PornCo, it's obvious where the public morality vote will lie, so that will be good for Amazon as well.
Having to put up the funds to sue Amazon defensively is pretty unfair. It does go to show that good IP protection can be a real asset. The settlement figure will no doubt be confidential but (happily for FyreTV) the amount will probably be figured off the value to Amazon not the cost to FyreTV. That could be very lucrative for them. Without the TM registrations, FyreTV would have a very difficult case ahead of them.
Amazon will settle or buy them out, they can't win this. I'm surprised they didn't foresee this and do something preemptively - like pick a different name.
Even if you want to say they didn't find them in the trademark database because of the spelling (doubtful, but possible), there is just no way they didn't check the domain name.
either a quick out of court settlement (which is most likely what the plaintiff is hoping for) or they will fight it since its not very likely that the low volume sale fyretv will be losing customers based on confusion of amazon's firetv