You shouldn't be so confident in your knowledge of the law, especially as it seems you have read none of it.
First, it does not matter if it is an unoccupied or incomplete dwelling. It does not matter if it is another kind of building or structure:
Georgia’s felony burglary statute
§16-7-1. Burglary
Home under construction qualifies for felony burglary purposes.
Smith v. State, 226 Ga. App. 9 (GA Ct. App. 1997)
Second, how do you know that they had "no knowledge" of any crime committed on any day by Arbery? The senior McMichael's lived right across the street from the house. The police department but the owner in touch with McMichael's and the owner had video on more than one occasion of Arbery in the house. A video clearly shows Arbery exiting the house, and running or fleeing it before the McMichael's were in pursuit.
Third, it does not matter that Arbery didn't find anything to steal or didn't take anything, if McMichael had a reasonable and probable suspicion (which is a lessor state of knowledge) to infer that was Arbery's purpose then that is sufficient. (Remember, McMichael before retirement had been an investigator on the illegal gun charge case involving Arbery).
Finally, of course the videos show a crime. Illegal entry without permission. That Arbery did it more than once is easily a basis of reasonable suspicion.
Here is the full set of laws laws you need to review so as to revise and inform your confidence:
Georgia’s citizens arrest statute:
§17-4-60 Grounds for arrest
Georgia’s justification statute (including use of force in making lawful arrest):
§16-3-20. Justification
Georgia’s felony burglary statute
§16-7-1. Burglary
Georgia’s aggravated assault statute:
§16-5-21. Aggravated assault
Georgia’s simple assault statute:
§ 16-5-20. Simple assault
Georgia’s open carry statute:
§ 16-11-126. Having or carrying handguns, long guns, or other weapons; license requirement; exceptions for homes, motor vehicles, private property, and other locations and conditions
Home under construction qualifies for felony burglary purposes.
Smith v. State, 226 Ga. App. 9 (GA Ct. App. 1997)
Assault requires an unlawful act.
Woodruff v. Woodruff, 22 Ga. 237 (GA Sup. Ct. 1857)