So there are a lot of different types of game designers. There isn't just one role called 'Game Designer.' It depends on what the activity is for sort of assembling the game and the way they want it to work.
There are content game designers. Those are people who write scripts and write quests. World builders are the people who assemble the world and that's often a shared role between the artists and the world builders, but the world builders tend to do more technical work, such as deciding that this is how these obstacles interact with each other. Make the trap spring open again and stuff.
Then there are systems designers and these are people who come up with the rules. When I shoot my gun and I hit somebody, how much damage does it do? They decide that if it's this gun, and you have this power up and they've got that much armor, then this formula says you get that much damage. And that's what a systems designer does.
Many times those systems designer are not only really proficient with things like Excel and Access, but also with scripting languages, because they might actually implement some of that code depending on the game in a scripting language and be responsible for how the game actually plays from a moment to moment basis.
Last you have either the creative director or lead designer depending on the scope and size of the project and the company. And that person's responsibility is the overall vision of the game, and making sure that it's well communicated in the beginning and throughout and that it sets and reaches the standards for the vision of the game as it was put out originally once it's shipped.