Translation:He is not late.
adjectives that end in ai, oi, ui, ii are called i adjectives and their endings change like the endings of verbs in plain form. So osokunai is the negative (present tense) form of the i adjective osoi. It already means late/slow all on its own but we still use desu with i adjectives because it is polite.
Subtle difference - おそくない is an adjective and is describing かれ. If you used おくれていません you would be talking about かれ is not doing ie. in the original it's saying he is not late (adjective), in your example with the verb it's more like saying he is not running late - that is, rather than describing him, you're stating the action that he is performing.