Burglary does not require that something is stolen, only that there is an intent to steal. If Arbery entered that building with the intent to steal, that is burglary. And, as has been alleged, Arbery had been suspected of previous break-ins, perhaps were items were stolen.
There is no evidence that Arbery intended to steal anything from that house. Under Georgia law, in order to make a citizens arrest, one must have witnessed a felony to have occurred or have immediate knowledge that a felony occurred. Neither father or son observed Arbery commit a felony nor did they have first hand knowledge that he had. They are going to prison for a long time.
As for being suspected of previous break-ins:
“While Gregory McMichael claimed Arbery looked like a suspect in a string of recent burglaries, Glynn County Police Lt. Cheri Bashlor told CNN this week just one automobile burglary in the neighborhood was reported when a 9 mm pistol was stolen January 1 from an unlocked truck outside the McMichaels’ home.”
https://www.cnn.com/2020/05/08/us/ahmaud-arbery-mcmichael-arrests-friday/index.html
As a jogger I have often stopped at homes under construction to take a pee. That was in the old days before it was required to have a portable toilet outside. Now every house has a portable toilet even before construction starts. Could he have gone in to relieve himself? Don’t know if there’s a portable toilet at that location. Jogging has its own set of dangers that I was always aware that some folks might think I was up to no good for running down their street.