Are Yemenis Arabs?
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Etymologically speaking, arrabiyun means to move around. The bedouin nomadic nations inhabited Southern Arabic as far as the history can tell. So yes, Yemeni people belong to the Semites and Southern-Arabic inhabitants are called Arabs these days. However, it is disputed whether they called themselves 'Arabs' during the BCE i.e. identified themselves using this particular term.
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You question omits the possibility for a concrete answer as the problem of national identification is multilateral. From my perspective what defines a nation is its language and culture, and Yemen historically shared the same culture as the rest of the Semitic nations of the South Arabia. Arabic language emerged from a variety of Old Semitic dialects and also included many branches until standardized between the 9th and 11th centuries during the Islamic conquests. Terms 'Semitic' and 'Arabic' are relative, since historically speaking Semitic sociology stems from the study of the history of many nations living in Ancient Mesopotamia, Arabian Peninsula a and possibly Ethiopia. From anthropological standpoint, what matters most is the language and the way of living of a particular society. And in case Yemeni history historically includes languages of South Arabia i.e. the so called Southern Arabic as well as the Ethiopian Semitic, one can say they stem from the same linguistic family.
From nationalistic position, anyone can claim they belong to a certain nation based on its political entity i.e. a nation state as something culturally and politically opposite. Nationalism in the Arab world emerged in the 19th century from what I can tell, during the late Ottoman Empire.