The doctrine of the ministry as taught in this part of Baier-Walther does not consider the “wider sense” to be a part of the Ecclesiastical Ministry.
The ecclesiastical ministry is defined thus: that it is a public office, ordained by God, in which certain persons, legitimately called and ordained, teach the Word of God, administer the sacraments, forgive and retain sins, and they care for and direct other things, which pertain to the church, and to the conversion, sanctification and eternal salvation of humans.
You can read it for yourself.
Was Walther’s doctrine incomplete as it was expressed here? (Why?)
Or, has the semantic and conceptual domain of “ecclesiastical ministry” been enlarged since then to include not only the office (position) that exists by our Lord’s command and institution, but also any activity that accomplishes the teaching of God’s Word?