Here is where Chromebooks might come up short for you. Also this is where Android compatibility really helps out.
I am not a big PC gamer, I prefer to use my Xbox. (I only have two games installed on that, Fallout 4 and Dishonered, and they are old games.) Still there are some quite good Android games that play well on Chromebooks. Currently I am starting out on Cultist Simulator, a card based Lovecraftian cult simulator. If slower, casual games are your cup of tea there are plenty of games to choose from on the Play Store.
Cloud based gaming is a thing and some Chromebooks have RGB gaming keyboards, high refresh rate displays and CPU suited to high powered gaming.
It should go without saying that Chromebooks are not best suited to professional level graphic design work. Once again there are Android apps which would work for casual use. Ibis Paint is one example of this type of app. Microsoft has recently announced that it will soon add an AI powered graphic design tool to 365. Microsoft Create will be a user friendly graphic design app that will probably run well on a Chromebook. Adobe has a large suite of cloud based graphic apps.