When you translate the sentence to Czech, you have to pay attention to Czech grammar. In this case, "Matěj je muž" would be correct to translate "Matěj is a man", since Czech grammar is your parameter here. But this exercise requires you to translate "Matěj je muž" to English, so you have to take English grammar into consideration, since, in English, the absence of the article 'a' in "Matěj is a man" would leave your sentence incorrect, hence why Duoling marked your answer as incorrect.
Duo's programming probably regards Matěj's" as the standard possessive for "belonging to Matěj" rather than as a contraction for "Matěj is." Standard contractions are accepted by default, while non-standard contractions need to be added manually to every possible sentence to make them acceptable. That can be very time-consuming for the small course team, especially when there are higher priorities.