I mean, theres clearly a semitic component to most Ethiopian civilisations such as Aksum and Abyssinia. Most Ethiopians speak a semitic language. There are ancient jewish, Christian and Islamic communities in the Ethiopian highlands. The politically dominant groups, namely the Habeshas believe they are the descendents of a union between Queen Sheba and Solomon. Ethiopian civilisations such as Dmt, Aksum and Abyssinia had stronger links to other Arabian civilisations such as the Sabaens than other SSA civilisations. And genetically, most seem to have semitic admixture.
It depends on what you mean by "intrinsically."
Actually only about half of Ethiopians speak a Semitic language as their mother language. The other half speak mostly speak Cushitic or Omotic languages; namely Oromo, Somali, Afar, Wolaita, Sidamo, Haddiyya, etc.
In terms of the origins of South Semitic Languages (i.e. Ge'ez, Amharic, Tigrinya, Tigre, Gurage, etc.), there is some debate about whether they originated in Ethiopia or South Arabia. This paper concludes that South Semitic Languages were introduced to Ethiopia approximately 3800 YBP from Southern Arabia. But an origin in Ethiopia is also widely considered.
Prior to the spread of South Semitic Languages into Ethiopia, it seems likely that many Ethiopians spoke Cushitic or Omotic languages. There are still pockets of Cushitic speakers (Agaw language speakers) in Northern Ethiopia and Eritrea, and its been proposed that Harari has a Sidamo substratum. There was also an Agaw speaking dynasty that ruled Northern Ethiopia from about 900 to 1300. In fact the rock churches of Lalibela were built this Agaw dynasty.
Genetically, there is also debate about how different genetically Semitic language speaking Ethiopians are from Cushitic speaking Ethiopians. Some studies have found differences that indicate Arabian influence; while other have found little difference between Semitic and Cushitic speaking populations, and little relationship to people in Southern Arabia.