Besides widgets and shortcodes, the other option for displaying data is custom templates. A custom template can be used for displaying custom post types, or you can create a page template for the basis of creating pages to display your data. By "page" I mean the WP post_type page, not any old generic webpage page.
Widgets are good for supplementary information shown in sidebars and footers or other such designated areas. Shortcodes are good for inserting data into regular post content. Custom post types are more of an organizational tool than a way to display data, but templates can easily be associated with them, which are exactly for displaying data.
Page templates are good for displaying data in a particular way as a complete page in of itself, contrasted with the typical WP index page that shows any number of various posts. Still, page templates can be made to do that as well. Templates are very flexible, but are not suited for inserting into post content.
From your brief description, I think a custom post type with a single page template is the way to go. Each game can be a post. All games can be listed on an archive page just like other posts would be. The single page can show the charts and all associated data in a single, nicely organized page for one particular game, much like finance data for a particular stock.