Survival games are a subgenre of action video games set in hostile, intense, open-world environments. Players generally begin with minimal equipment and are required to survive as long as possible by crafting tools, weapons, shelters, and collecting resources. Many survival games are based on randomly or procedurally generated persistent environments; more recently, survival games are often playable online, allowing players to interact in a single world. Survival games are generally open-ended with no set goals and often closely related to the survival horror genre, where the player must survive within a supernatural setting, such as a zombie apocalypse.
According to wikipedia:
"Survival horror is a subgenre of action-adventure and horror video games that focuses on survival of the character as the game tries to frighten players with either horror graphics or scary ambiance. Although combat can be part of the gameplay, the player is made to feel less in control than in typical action games through limited ammunition, health, speed and vision, or through various obstructions of the player's interaction with the game mechanics. The player is also challenged to find items that unlock the path to new areas and solve puzzles to proceed in the game. Games make use of strong horror themes, like dark mazelike environments and unexpected attacks from enemies."
https://en.wikipedia.org/wiki/Survival_horror
You're not wrong, but you took a very roundabout manner to explain the concept and yet didn't really do it much justice.
Uhh, the first line literally says (to quote) "Saiko No Sutoka is a Horror Survival Game". Both "Horror" and "Survival" are there.
I think you're mistaking the wording as meaning something else: if it was a pure Survival game then the Horror term wouldn't be added. As far as definitions and gameplay, this follows the same principles as a game like Alien: Isolation since you have little/no way to fight against your adversary while they can (easily) kill you, for example. Survival might be the "Parent Genre" but Survival Horror is specific to this style of "Survival" games: induce fear, offer a feeling of powerlessness, solve a set of puzzles to progress and avoid your adversary as much as you can.