WordPress is a pain in many ways. It has had some of the most outrageous security problems in the industry. It is written in one of the slowest languages available (PHP is slower than Python, only Ruby is slower than PHP!) It hits the database really hard for everything, making it even slower. Its extension model is a combination between way too low level (CSS that must match up to their chosen tag format, etc) and too high level (functions with magical names do magical things in magical contexts.)
Sure, you can build a system on top of WordPress. And you can install a forum. And you can write some kind of authorization plugin that works for your game (or maybe there even exists some plugin you can use for this -- WordPress does have a lot of plugins!) Some measurements also say that 60% of all websites use WordPress! That's generally speaking the worst 60%, mind you, and includes tons of SEO spam, because it's so easy to create fake websites on WordPress hosts, but it's still an impressive number. It is totally possible to do, and it's unlikely to be the limiting factor for adoption of your game -- your game itself is quite likely to be the main challenge, all things considering.
But if there's any other option, I would look at those for comparison. How about a Facebook page as your user forum, and using "sign in with Facebook" and some kind of oauth2 solution? (That will be hard if your game doesn't embed a browser, of course.) How about one of the general back-end solutions, like Google Firebase, or AWS Amplify, or whatever? If you were on mobile, Google Play Services would be obvious, but for PC, it's not a convenient solution. How about Steamworks?
If you're not looking for a hosted solution, just ready-made software, tons of other options exist, including Django (Python,) Drupal (PHP) and Discourse (Ruby.) Or start with a forum you like that you can install, and build an alternative web service that the game can use to verify username/password.