This special treatment stemmed from the perception of sport as that of a special activity with modest economic effects.

What is the function of that of in this sentence?

‘That’ is a pronoun here. It is the same as ‘one.’

‘That’ follows ‘as,’ which is a preposition here. It is similar to ‘like,’ but ‘like’ means ‘similar to,’ while ‘as’ means ‘exactly like,’ or ‘equaling.’

‘Of a special activity’ modifies ‘that.’ ‘With modest economic effects’ modifies ‘activity.’

So, ‘that’ is the first word of a phrase that follows the preposition ‘as.’ ‘Of’ introduces some modification. ‘That of’ would always be followed by another noun phrase, which describes ‘that.’

quote:

This special treatment stemmed from the perception of sport as that of a special activity with modest economic effects.

In re-reading this sentence, I think it would be better to omit 'that of' entirely:

This special treatment stemmed from the perception of sport as a special activity with modest economic effects.

This would be the most direct.