Yes, American cheese is cheese.
There are artificial cheese slices but there is also soy cheese and almond cheese and I don't know what vegan cheese.
Velveeta is not legally cheese because it has Milk Protein Concentrate in it. Yep, you read that correctly. If you add milk protein (which is made from MILK) to cheese (which is made from MILK) it is no longer cheese. The ways of the FDA are mysterious and sort of stupid. You want to read something that will make you want to cry go read the story about the farmer who took them to court to keep from being forced to label his straight from the cow milk with cream removed as artificial milk because it was not fortified. You will cry, you will laugh, you will wonder what kind of morons run the FDA.
But to return to your question yes, unless you buy the artificial stuff deliberately American cheese is cheese. Even the FDA says so but what do they know.
I know a lot of it that they sell is artificial.
Some kind of hydrogenated oil, cheese product with stabilizers.
“individually wrapped” ;)
Gubermint shut down a friend of mine for selling raw un pasteurized milk which he advertised as such