I'm not entirely sure what they mean here, but we usually speak of 'grammatical function' - not 'functioning' or anything else. It makes sense in this context.

Examples of similar contexts:

www.thefreedictionary.com/Grammatical function‎
TheFreeDictionary.com
But it seems that the bias against having SUB and IN markers and **their combinations in grammatical function** is just an arbitrary fact of the Tsezic languages.

connection.ebscohost.com/.../verb-type-animacy-definiteness-grammatic...‎
EBSCOhost serves thousands of libraries with premium essays, articles and other content **including Verb type, animacy and definiteness in grammatical function** ...

https://slavica.indiana.edu/.../Grammatical_Function_Syntact...‎
The study concludes with an explicit statement of **the distinction in grammatical function** signalled by detachment.