Hi,
Let me see if i understand what you are saying. in the google structured data testing tool you see URLs that say something like https://www.yoursite.com/2014/09/06/post-name/ ?
you might be able to change this to https://www.yoursite.com/game-review/post-name/ by selecting and editing custom structure under Settings > Permalinks in the WordPress dashboard. in the custom structure field you would want to put:
/game-review/%postname%/
this will mean all your blog posts will go under the url yoursite.com/game-review/post-name/ where post-name will be the name you give to the post.
If you want to go a little further, you could create a custom post type, this will allow you to tell WordPress that you are not writing posts, you are writing game reviews, and then Google will not mistake it for a news article (if thats what you are worried about)
The plugin you referenced allows you to switch between existing post types. So this plugin wont create new post types.
Consider creating a custom post type called ‘Games’ or ‘Game Review’ and make this custom post type similar to a Page or Post except now you can see it in the URL as game and you will be able to use categories and tags for games, also people will be able to view an archive of game articles and optionally organize that archive by tag or category, and at the same time you could still use posts and pages if and when you need to.
to get started with custom post types install the plugin wp-types and read the WordPress codex on Custom Post Types