Well the article is wrong on the "one baptism" not being the water immersion.
There is the singular teaching of "baptisms". The water, the Holy Spirit and fire.
Two of the "one's" are "baptism" and "Spirit." To claim the one Spirit is the one baptism is to count the Spirit twice.
I would add that the author paints with a broad brush, and sometimes contradictory information.
If the church is traced back to Jesus calling the disciples in Galilee (a common idea) it did not begin with John the Baptist (a claim I have never heard any landmark Baptist make, but which they are often accused of).
The author equates landmarkism with Baptist Bridism. While possibly all Baptist Briders would be landmarkers, not all landmarkers hold the Baptist Bride view.
This is not a universal position among landmark Baptists. It might be the predominant view (not sure), but many landmark Baptists make scriptural baptism, not local church membership, the prerequisite for the Lord's supper.
Partially true. Baptists who held some or all of these views obtained the label pejoratively (which they themselves embraced) after J. M. Pendleton wrote An Old Landmark Reset. Further, various researchers (such as Thomas Williamson) have shown the existence of these beliefs among Baptists long before 1851, J.R. Graves, and J. M. Pendleton. What J. R. Graves was successful in doing, in my opinion, was in synthesizing certain Baptist ecclesiological beliefs into one unified theological system (i.e., Landmarkism is a logical ecclesiological system is the same sense Calvinism is a logical soteriological system, premillennialism is a logical eschatological system, etc.).