Games console given without wrapping -- that's mean (6)
I believe the answer is:
intend
'that's mean' is the definition.
(to intend to something is to mean it)
'games console given without wrapping' is the wordplay.
'games console' becomes 'Nintendo' (brand of video game console).
'given without wrapping' says to take the centre (the letters wrapping up the word are removed).
The middle of 'nintendo' is 'INTEND'.
(Other definitions for intend that I've seen before include "1 dn [DESIGN]" , "Mean - purpose" , "Have as purpose or plan" , "Purport" , "Plan, propose" .)