The first time I got this, I answered "I play by myself." I would consider this the exact same meaning.
Almost same meaning, different ways of expressing it.
Closer to your sentence maybe would be 나는 혼자 놀아요?
I agree with the reply, simply for semantic accuracy. Separately would imply there are others nearby who are also playing, whereas playing all by myself is simply a sad reminder of the majority of my childhood. Different meanings, surely.
The word '따로놀다' exists as an idiom which means 'does not get along'. Please consider modifying the translation to '저는 혼자 놉니다' or '저는 분리되어 놉니다'. I know this sounds weird. but it's because the original sentence is weird after all...
i think this sentence can makes you feel hard. 따로 means separately, part of the other. not like by myself or alone.