Does this sentence work?
I never played computer games in the past, but since last month I do.
If it does, does it omit an implied part, which is
(since last month) I have been playing and (I do)
It doesn't omit the implied part.
Maybe something like this will work better:
I have never played computer games in the past, but since the last month, I have been.
or
I only just started playing computer games, since the last month.
EDIT: Kate's version is better. I completely forgot that the word "had" existed.