In my 15-Minute Parenting books I talk about Dimension Play, which is taken from the Theraplay Modality (Theraplay.org). This type of play is about communicating in a "doing" rather than "saying" way.

There are 4 Dimensions here:

Structure: This is play that communicates clearly what is expected and provides a sense of safety in there being clear boundaries and scaffolding. It conveys a sense of "you are safe and there is somebody bigger and kind who can take care of you and ensure that you and this situation doesn't get out of control"

Engagement: This play is about bringing the energy levels of the situation/child up or down (likely up and then down and back up and back down in a type of emotional regulatory rollercoaster). This is about having fun together and conveying the message that "you are fun and I like being with you". In order for children to grow up and know how to experience joy in others they have to experience being enjoyed by others. This type of play is all about that. It also is a great way to build on a child's capacity for prolonged engagement by gradually extending an activity a bit longer each time you play.

Nurture: This type of play is about conveying that "you are worthy of good care and there is always someone here to take care of you".  This is a gentler, slower, calmer way of playing and involves touch, feeding, rocking, singing and swaying.

Challenge: This type of play is about building a child's sense of self-esteem, self-worth and self-efficacy.  It conveys "wow, look at all you are capable of doing" and it challenges a child to stretch themselves a little, not a lot, outside of their comfort zone to try new things, take mild risks and see that this is something worth doing.  Always focus on praising effort over outcome and to this end ensure that your challenge activities are more collaborative than competitive in focus.

You will find lots of examples of these stages and dimensions of play in my 1st book 15 Minute-Parenting 0-7 years and in my 15-Minute Parenting 8-12 years I show you how to grow this play up in line with your child's growing up.  I also talk about this on my 15-Minute Parenting Podcast