So, having finally finished the game, I thought I'd post my thoughts on it.
In my opinion, there comes a point in a game's existence where it simply grows too old to be tolerated in its current form. The standards that were in place at the time of its creation have crossed a certain event horizon and are just too antiquated in comparison to what is around in present day. Naturally, this also sets a certain bar for any remake that a game in question might have, and said bar dictates how close a remake can remain to its source material before it starts to deviate for the purpose of said remake's existence, namely being a version of the old game that is on more modern standards. In other words, this bar is what decides how modernized a game's remake must be to be viewed as an acceptable replacement by modern definitions. And this also means that the older the game is the lower the bar is.
All of this can be summurized to say that Fire Emblem Gaiden, being what it is and not being graced with a modern remake, sets its bar pretty low. And such, despite any flaws that this remake might have, I consider it an acceptable replacement for the original and would recommend to at least try it if you couldn't stomach the original game.