I've been in development for 30+ years, and was QA for about 15 of that (also QA manager, and director of engineering, hiring both QA and developers.)
If you can get a QA job -- if you have tenacity, attention to detail, and can reliably show up for work -- then, yes, it's a fairly "easy" way to get a foot in the door.
However, do NOT fall for the romantic notion that game-tester means you "play games all day long." In fact, many people who become game-testers find that they come to really hate playing games in their spare time, as it "feels too much like work." In game testing, you may be asked to do things like
Play the same level 800 times until you can figure out the exact steps needed to make it mis-behave like it seems to about 1-in-50 times.
Skip all the cool parts of game-X and play this boring side-quest that nobody will ever do, because we need someone to test it.
Write-up your findings in excruciating detail, such that someone else can step-through your instructions and see exactly what you saw, but without asking anyone any questions -- they have to be able to do it from just your written instructions.
Also, you need to be passionate, but without too much ego. That is, you have to care enough to want to make things better, but ok with frequent shooting-down of your ideas for improvement, and not let it drive you bonkers.
Back to your original question: what makes being software-QA (games or otherwise) an easy entry-level position is that the skill-set is something that anyone can develop, and doesn't require a lot of schooling. As above, tenacity, attention to detail and reliability are more important than many technical skills.
It's also a good growth position. It's easy for a motivated person to go from "entry level QA" to "lead tester" in just a couple of years, and promotion opportunities are many.
While it CAN lead to a development position, typically QA and developer skill sets are very different.
It's also a lot of hard, frustrating work. It is NOT "playing games all day long"! Some folks love it, some folks leave to do something more enjoyable, like flipping burgers. The difference lies with the individual more than with the job.
Btw, if you want to beef up your resume for an entry-level game-tester position, volunteer to do some beta-testing for games online, and learn how to write a decent bug report. (You can Google this. A good report is not "paladins suck" or "the space orb needs nerfed." Find out what it means to write a good bug report and then go out and write some. When you go to a job interview, take along 2-3 of your best to show, and explain that you have no professional training, but that this is what you were able to learn on your own. That's valuable skills, right there.