Or HaChaim on Exodus 21:21/אור החיים על שמות כ״א:כ״א

1 לא יקם כי בספו הוא, he will not be avenged for it was his own money. If he killed the slave unintentionally (in the accepted sense of the word), the master will have to be confined in a city of refuge on account of this. In this ruling there is no difference between putting to death of one's slave or some other human being. Exile is applicable only if one killed directly, in accordance with the definitions we outlined in verse 12. The Torah only needed to write in which respect the law of a master killing a slave is different from someone who kills a person who is not his slave.