Is it good for my baby to have alone time or do I need to play with him constantly?

Yes. Every baby, and every child, needs quiet time, separate from sleep time. Whereas it's great fun to make a baby laugh, you will notice that whatever you are doing to get that belly laugh will eventually over-stimulate your baby and make them cry. You do not need to play with him constantly. You will both enjoy the quiet times too.
Yes. It is good for the baby to have alone time. During this time, he will learn to self-console, learn to explore his immediate environment and you may hear a contented babbling during this time. You should still attend to any needs, like hunger or pain, and he definitely needs his time with you, too. Often a baby will show signs when he needs less stimulation, like gaze avoidance.