To start, I've never really found a hard and fast "best" answer here in terms of which setup will help you the most with Google. I've gone both routes and been able to get sites ranking in Google either way. You can be penalized for keyword stuffing (and other reasons) no matter what direction you go.
Now, that said, in general, if you are looking at what is best for SEO purposes, I have found it is better to go with a sub-directory instead of a sub-domain, especially if you are going to cross promote content (people interested in one game will probably be interested in information you have on another game, right?).
When it comes to the SEO benefit, I'd recommend the sub-directory not because a sub-domain is bad, but it is that you have a lot to gain by using a sub-directory. Google generally views sub-domains as separate websites, and each separate website has separate rankings signals (like links).
For example, any links pointing to
callofduty.example.com won't really help
grandtheftauto.example.com because those are two different websites (generally speaking, there are always exceptions). However, any links pointing to
example.com/callofduty could help the pages in the directory
example.com/grandtheftauto gain rankings because those are all pages on
This starts to matter especially at scale for traffic, and it sounds like you are going to have some scale. Let's say you start with 50 of these as sub-domains. You put in the work, get good rankings and a decent amount of traffic for all 50. You decide to add your 51st video game onto your site. If you had done the first 50 as a sub-domain, then that 51st will require as much investment (more than likely) to get it ranking. If you do this as a sub-directory, though, then the 51st one you add will be easier to rank because those pages will just be new pages on the same domain as the other 50. With the sub-directory setup, you have one massively awesome site with 51 video games on it. With the sub-domain setup, you have 51 websites.
Here is a video from a few months back with more info about this topic and more explanation on link equity passing. It seems to be the most current info on this topic, and the one I've seen referenced the most by people in the tech SEO world: