Simple drawing games are normally a hit with children 5+. These are a few that I have in my toolbox; if your child is a big drawer you should encourage them to create more games!
1. Drawing portraits of each other without looking at the paper. Variation: not being able to lift the pen from the paper.
2. The squiggle game. Originally invented by child psychoanalyst Donald Winnicott as a way for children to communicate their thoughts and feelings, this game can be a lot of fun. All the players draw random squiggles and pass them onto the next player who turns their squiggle into something.
3. Picture consequences (pictured above). A classic game you probably already know of where an image of a person is drawn in sections. Everyone starts by drawing a head, folds their paper over and passes the paper to their neighbour (leaving a little hint of the neck visible) who draws the body and folds it over and passes it on again (leaving a bit of the waist visible). Then their neighbour finishes with the legs and feet. Afterwards everyone opens the papers to reveal the surreal characters they have created.
4. 'Telestrations' or 'Whispernary'. This game for 3 or more players is a visual equivalent of 'the telephone game', which used to be called 'chinese whispers'. Everyone writes a sentence, an object or a phrase on a piece of paper and passes it to their neighbour who then folds over the writing and attempts to draw a picture that communicates the phrase. They pass their paper to their neighbour who folds over the picture and writes the phrase, sentence or object they think the picture represents. This process is repeated until each player ends up with their original paper. Similarly to picture consequences, the images and sentences take a surreal turn which children absolutely love.
5. Parallel drawings. In this activity, the idea is to draw separate pictures but with the same content, while keeping their pictures hidden from each other. Each artist takes a turn to say what everyone should add to their picture, e.g. one person says 'everyone draw a monkey' and the next person 'the monkey is eating a banana', followed by 'above the monkey is a cloud and it is raining'... In the end everyone shows their pictures to each other, noticing the similarities and differences of what they have created.
6. Fantasy towns. In this activity, each child creates a map of the fantasy town of their dreams. You can brainstorm first what kind of features could be in a fantasy town (Where/what will people eat? What can they do for fun? How do they get around?) At the end I normally get the child to give me a tour of the town and then tell the child what I would do on my perfect day in the town, step by step (e.g. I would start by eating breakfast at the chocolate fountain, then I would go by hovercraft to the cinema etc)