It's very easy to challenge someone from the Topic Page. Please follow these steps:
Enter a topic page by tapping a topic icon. On the topic page you have 3 options next to the topic icon:
Tap the Play button and you´ll enter the challenge screen where you can either tap Play Now to matchup with a random opponent, or choose your opponent from your list of friends.
You can search through your friends in the search bar, or select a friend from the suggestions below. (see picture)