There are different levels of competence in connecting during play (or connecting any time, for that matter), based on the child's developmental level.
Physical coregulation the most basic level. Does not require facial or verbal engagement. Child realizes that his actions impact yours and vice versa and is able to participate in simple coregulated, back and forth patterns such as row, row, row your boat..Facial emotion sharing must be mutual. Child cannot be smiling randomly. Child should react to your genuine smile with a return smile (and vice versa).
Facial referencing for feedback Child seeks out your face to continue play when you pause or create a situation of uncertainty for him.
Physical coordination Child is able to physically coordinate with you in play schemes, such as ring around the rosy, mexican hat dance, clapping games.
Competence in role actions with variations Child is able to participate competently in play schemes where he has a defined role in a patterned interaction and is able to adapt to small variations in his role (child's role is to hand you blocks to build a tower, you move to different places around the room and the child goes to you to hand you the blocks adjusts to the variation in your location.)
Repair actions: Child takes repair actions when play is interrupted or pattern is disrupted, such as running to get a stray ball and bringing it back to resume the play, tugging on mom or saying "come on" when mom purposely pauses play, etc.
Child initiates play Comes to you and asks to play together.
The higher the level of the child's connection, the less "work" the parent feels he has to do to encourage the connection.
(the above competencies) all are competencies developed under age 2 for NT kids. Most NT kids are competent in these areas by about 18 months, except possibly physical coordination. Even social repair actions occur in NT babies significantly under age 1, such as in Dr. Tronick's famous still face experiment. It's amazing how early in life that NT kids achieve these types of social competence.