If Amazon was offered the opportunity to sell one prime subscription OR one Fire TV 4K surely they would choose to sell the Prime subscription. Yes, the Fire TV would give them the opportunity to sell apps and content but the Prime subscription would lock in that customer to make the majority of their purchases for the following year from Amazon. If they had already paid for fast shipping with Amazon, why shop elsewhere - even if Amazon is a few £/$ more expensive?
With this in mind, by not releasing a Prime Video app for other boxes, to me Amazon is effectively opting to sell the Fire TV rather than try and sell a Prime subscription. People who have an AppleTV, Roku or other non-Amazon box are surely less likely to take out a Prime subscription if they can't view Prime videos on their TV conveniently. By not having a Prime subscription I would argue that they are also more likely to be less exclusive to Amazon for their other purchases too.
My guess is Amazon is hoping people will go with a Prime subscription and then pick up a FireTV but I think if their strategy hasn't worked by the Summer we will see a Prime Videos app befor the end of the year.