Embed own pages into posts

I have this WP installation covering news about different video games. I’d like to have a fact page about each and every game, and to embed at least a few paragraphs from this page into every new post about it.

I’ve been using the oembed thing a lot for embedding stuff from other sites, and it looks like exactly what I’d like to be using, but from what I can gather, only a few sites are supported by oembed. When I try to paste the link to my own page, it won’t embed.

Is there any way to get this working without a lot of coding (which I’m not that big on)?