More context please.

You ask a child if he wants to play train, possibly imitaing a condutor, or just with a train or many.

If the child will be imitating a train, or pretending to be someone working on the railway, I would say "Do you want to play trains?"

If the child will be playing with a toy train, I would say "Do you want to play with your (toy) train?"

If both conditions are true then you can use either.

Thank you, GPY.

That means you don't use the singular form. Is there any reasons?

One more thing, you want to pretend getting into a rocketship and flying into space. Would you say "play rocketship" or "play rocketships"?

I would use the plural in the "rocketship(s)" case too. I suppose I imagine that more than one vehicle is involved. Or perhaps it just feels more idiomatic for no obvious reason.

Thank you. But you play jump rope, right? Singular?

onizoThank you. But you play jump rope, right? Singular?

I believe so, although "jump rope" is AmE not used in the UK, so I would not use that myself.