Hi Jan,
Ok, I see what you mean. Well, this is purely a css issue — you wouldn’t have to touch any php file to reproduce a similar style as the html structure should be identical in both sites you showed me.
In Events > Settings > Display tab, you can select Tribe Events Styles as your Default stylesheet used for events templates. That way, your calendar would look a lot more like the one on our demo site 🙂
I hope this helps,
Cheers,
Jeremy