What “dispensation” means here
The word refers to an administration, stewardship, or ordered arrangement. Paul is describing God’s administration of His purpose when the appointed times reach their fulfilment.
The verse is not presenting history as uncontrolled. It portrays God directing His purpose toward a determined conclusion centred in Christ.
The fulness of times
“Fulness” indicates completion: the times have reached the point appointed for God’s purpose. A related expression appears in Galatians 4:4 concerning the sending of God’s Son when the fulness of the time was come.
In Ephesians 1 the expression looks toward the comprehensive completion of God’s plan, not only the first coming of Christ.
All things gathered in Christ
The scope includes things in heaven and things on earth. Sin has produced alienation, disorder, and hostility, but God’s purpose is that Christ should have the preeminence and that the created order should find its proper unity under Him.
This does not erase every distinction or teach salvation apart from faith. The emphasis is Christ’s universal headship and the final accomplishment of God’s purpose through Him.