I think you may need to work on strategies for joining in with him at home. This is not necessarily simple, sometimes you have to "break in" to a game.
But he'll need lots of practice at understanding the fun of doing things together with people he loves before he can do it with complete strangers/other kids with their own needs.
What kind of games does he play?
he may find the singing/reading stuff easier because the rules are clear and don't keep changing. (like jigsaws).
pre-school may also be able to help. My son eventually got lots of help from the nursery within what's now his school at 3. But the local parent-run parent-funded private pre-school didn't have the expertise to really help. I think nurseries attached to schools are ideal because the staff are or have access to highly qualified professional teachers who know exactly what social skills they want the child to have by the time he starts in reception.
He plays lots of imagining games... Pretends to be an astronaut / driver / bear! He often just likes running around with a vehicle making the noise it makes. He loves baking and drawing with me. He likes playing chase and play fighting with his dad.
What kind of games do people play with their 3 year old boys?
I sometimes worry that his little sister annoys him so much that she has made him prefer his own company.