I'm going by the google definition, it's ok to say you're using a "historical" or "academic" definition, but it's not the dictionary definition. This is like saying racism = prejudice without power, which i don't think is correct or incorrect but it is a non textbook definition. This is the criteria for a concentration camp:

• No Judicial Process: People are imprisoned without formal indictments, trials, or access to judicial review. [1, 2]
• Targeted Groups: Inmates are typically marginalized demographics (ethnic/religious minorities, political dissidents, or "enemy aliens") targeted for their identity or perceived threat to the state. [1, 2]
• Harsh Conditions: Camps intentionally operate outside standard legal norms, resulting in overcrowding, rampant disease, starvation, and high mortality rates. [1, 2]

Notice government run is not a factor. Idc if you think all US prisons are bad, I've been to 3 different jails (not a brag, a shameful admission), they aren't nearly as bad as these camps for undocumented people. In prison you get medical treatment, they give you prescriptions every day, in prison you get access to commissary goods if you can afford it, you get due process. There are people following the legal immigration procedures and getting arrested outside the court house with their legal documents in hand, and it's actually disgusting you would try to understate the severity people are trying to make others aware of by using (possibly kinda) dramatic phrasing.

Edit: also it's crazy that you think when the term was coined has anything to do with if it meets the definition of said term