Perhaps this explanation will help. When I hear the word 'Sahara' I think of a physical place, in northern Africa. When I hear the word 'desert' I think of an ecological system, characterized primarily by low rainfall and sandy soils. When I think of the physical place in northern Africa that is denoted (in my language) by the word 'Sahara', I think of it as being an exemplar of the ecological system denoted by the word 'desert'.

Near me, there's the Sonoran desert and the Great Basin desert. If I lived in eastern Asia I might think of the Gobi desert. There's many deserts. So while I take your point that 'Sahara', in a non-English language, denotes what I call in English 'desert', I would say that the phrase 'Sahara desert' could be interpreted to signify "the place on this planet, that could be characterized as having a desert ecosystem, that is described by the people who live nearby as 'Sahara'". For the people who do not know that 'Sahara' is used by some other people to denote what they think of when they say the word 'desert', the word 'desert' is not extraneous. But for you, who does, it is.