After successful stops in Italy, Spain and Turkey, the 2007 NBA Europe Live Tour comes to an end right here in England, the country where basketball has yet to take off.
the fragment in red means that people need to work hard to promote basketball, i.e. basketball is NOT quite popular NOW. or basketball has already been popular, though for a not quite lone peiod?
Yet is used in negative when you talk about something that has not happened but that you expect to happen for example we have yet to decide what action to take means that we have not decided what action to take.
Accordingly, the meaning would be basketball is not quite popular right now.
PS This explanation is taken from Oxford Dictionary
'yet' means 'up until the present'.
Although is a MAJOR sport in the States, few people take an interest in or play the sport in the UK. 'yet to take off' indicates that it is not popular here currently, (but may become so some time in the future.)