I won't talk about Civ and similiar games because they are a completely different thing. Same can be said about RTS games, they are a completely different genre (that i love and used to play alot)
however, the reason i prefer FE over other SRPG
Game Speed: FE games are relatively fast & responsive compared to most other SRPG. Units have high lethality, leading to fast tactical gameplay
Simple to leart, hard to master: The Mechanics of FE are pretty simple to learn, and in a game they get progressively more complex (by adding more skills and terrain, for example), they don't throw everything at you at once. Despite the ease of access, everyone plays FE in their own way and there are numerous tactics out there for every chapter.
Perma death, especially in harder games, means your every move matters.
The amount of units you control. In FE, you control from 5 units early game up to 15 late game, making the scale feel big. Alot of SRPG stick you with 4-6 units, making it more like a overglorified RPG battle
Access to information: A single look at the stat screen and you can calculat everything in FE. Other SRPG make calculations way more complex and have numbers in the 1000s that make me go ''wtf? How am i suppossed to calculate that?''
I prefer FE's Map design over most SRPG as well
There are a couple more reasons as well, i am sure, but those are the ones from the top of my head
You talked about Chess, and i love FE exactly because it's like Chess.