Support conversations, plot advancement done by completing missions (and the plot is actually quite substantial outside FEDS), following the story of the main character (or in FE7 the advisor)...
None of this sounds familiar or meets the criteria?
I would argue not. Plot advancement is linear (not taking into account what AlexX mentioned above on split paths) - you can't choose to
not advance the plot without not playing the game, support conversations are also linear, and there is no player input in what happens in them. That said, there's input in
which support conversations occur, but that's more storybuilding than roleplaying (admittedly, this critereon does reasonably qualify for RPG elements).
As for following the story of the main character... That's just the flow of narrative, and has no bearing on whether it's an RPG or not.
To be fair, the term 'RPG' is quite poorly-defined these days anyway, and what is to one person an RPG is an Action-Adventure to another. Hell, Bioshock has RPG elements, but I rarely see it being called that. What I'm saying is - if the people making the game want to call it an RPG, and it just might qualify for a few RPG criteria, I won't argue - there's plenty more interesting things to say about Fire Emblem anyway.