Wife drawn in by computer games gets immersed (5)

I believe the answer is:

swims

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'computer games gets immersed' is the definition.
I can't tell whether this defines the answer.

'wife drawn in' is the wordplay.
'wife' becomes 'w' (abbreviation).
'drawn' becomes 'sims' (I am not sure about this - if you are sure you should believe this answer much more).
'in' means one lot of letters goes inside another.
'w' placed inside 'sims' is 'SWIMS'.

'by' is the link.

Can you help me to learn more?

I've seen this clue in The Independent.

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