That argument doesn't follow. As in English, the definite article pertains to the identifiability of the noun; it doesn't indicate whether the noun is internally a composite or not. An individual can be identifiable as well as a class. The NT is filled with hundreds of references to ho Khristos "the Christ". Those references have unique reference to a single individual, Jesus. It can also refer to groups or classes, such as ho dikaioi "the righteous" (Matthew 25:37) or ho ponèroi "the wicked" (13:49). The quote above states: "Other references in bible refer to individuals being slaves and stewards, but not THE slave/steward". I'm not sure what this is supposed to even mean. Slave/steward is a relational term, one is the slave/steward for someone else (the master), so individuals mentioned in the Bible as slaves and stewards are THE slave/steward for someone. Moses was "the servant of the Lord (ho doulos kuriou)" (2 Kings 18:12 LXX), David was "the servant of Saul (ho doulos Saoul)" (1 Samuel 29:3 LXX), etc.; note the definite article in these examples. The Society seems to take "the slave" to be a title (like ho Khristos "the Christ", which has unique reference), and that is what contrasts with other references to slaves or stewards in the Bible, but the expression is definitely not used as a title in the actual parable. The parable refers to the steward in relational terms as the one whom his master (ho kurios) has given responsibility over certain household duties.
It was common parabolic style to refer to the main characters in the parable in definite terms (since parables dramatize certain situations rather than have generic reference as in aphorisms and proverbs). So for instance the parable of the sower begins: "The sower (ho speiròn) went out to sow, etc." (Matthew 13:3); one could instead say "A sower went out to sow" (as some translations put it in English), but the definite article is used. Another example can be found in the parable of the thief in the immediately preceding verses: "But know this that if the householder (ho oikodespotès) had known in what part of night the thief (ho kleptès) would be coming, he would have watched and would not have let his house get broken into". There are many other examples in parables and this is commonly understood as reflecting underlying Semitic diction in the original oral Aramaic form of the parables (specifically, the emphatic state). As Joachim Jeremias noted: "The usage is characteristic of Semitic imagery. Already we find in the OT the use of the definite article with an indefinite meaning often in parables and pictorial narratives. In such cases the Semite thinks pictorially and has an image in his mind of a concrete instance, though he may be speaking of a general phenomenon" (The Parables of Jesus, 1972, p. 11). There is also of course the fact that the first mention of the slave in the parable was in a question concerning identification, which also promotes the use of the definite. The parable of the sower could have been phrased similarly: "Who is the sower who went to sow his field? He was scattering the seed and some fell along the path, etc." (But the focus of that parable was not whom the sower represents but the different eventualities that could occur)