There are a million ways to get into the industry and hundreds of ways to get into each role. I think if you show a proficiency in any area they will consider you for that role.
Software Engineering gives you a good overarching understanding of software development. I studied computer science with a “concentration” in software engineering (essentially a distinction on my degree when I took 8 software engineering classes). Think of computer science as giving you the baseline understanding of programming, compilers, hardware (in terms of chipset design), AI, maths, etc. and SE in understanding how software comes together through requirements gathering, planning, coordination, testing, and so on.
Think of baking a cake with 30 other people. There is a lot of coordination that needs to happen for it to go smoothly. On top of that you have to make sure you’re making the right sort of cake, and that the cake holds up to certain standards. That’s where the importance of software engineering lies.
So I don’t think it lends itself particularly well to a coding job, but if in your classes you show a profficiency for coding it is something you can build upon in your spare time to land that coding job.
Coding is one of the many, many jobs required to create a game. If that truly is the one thing that you really like to do then I would suggest looking at some coding specific classes or courses after you’ve done this one.
There’s more I can say but I have a few questions for you so I can focus my statements to be relevant to your situation: what do you find appealing about coding in particular? Does the idea of creating an inventory system for a character something you find appealing? How about ensuring that a weapons projectile physics works properly? How about coding an emote wheel where a player can choose and perform an emote?
In some cases people mix up “coding” with “design”, and it’s likely you haven’t but I want to put this out there in case anyone else reading this is interested, but a design role puts one in a position where they create how the gameplay/controls work, what sort of stuff the character can carry in their inventory, how the weapons work, etc. So maybe a design wall would appeal to you a bit more? Ironically to demonstrate proficiency in design you have to know how to code your own stuff to kind of show that you can do it, but the distinction is something to keep in mind.
I haven’t looked at how these large developers hire people but I get the impression that your relevant education takes a backseat to your portfolio. Like with any job where you create stuff, you need to have a decent portfolio of your own stuff to show.
So say you take this course (and maybe if you other courses after) and then you use engines like Unity or Unreal Engine to help you create some games, prototypes, and Game Jam entries. I think you will find you will learn as much in that phase as you will in the formal education phase. This portfolio shows everyone that you are adept at certain parts of game development.