This is a common construction in signs, notices, terms and conditions and similar contexts where clarity and brevity is essential.

It could be seen as an elliptical form of something like this:

'adults <em>whose </em>age <em>is </em>19 years and older'

Hello Balint Pataki,

This is a very good question.

I'm not a native speaker, but to me 'age' sounds as if it is here a part of the adjective phrase.

I've seen it several times in the same context, so I find it okay. I also think 'aged' has the same meaning as old, whereas 'age' focuses on the current number of years.

I hope this helps. Have a good day!

Best regards,

Maria