"The Isle of Man is not in the United Kingdom."
Translation:Chan eil Eilean Mhanainn anns an Rìoghachd Aonaichte.
The simple answer is that the name of that island needs the definite article in English - 'the Isle of Man', but not in Gaelic - Eilean Mhanainn. The names of some islands need the definite article, e.g. an t-Eilean Sgitheanach (Skye), others don't need the definite article, e.g. Eilean Mhanainn. These can be learned as you go.
The longer answer (which might not mean much at this stage, as we haven't met the genitive case yet, so don't worry if it seems confusing) is that the names of islands that use the form "eilean + adjective" need the definite article before eilean, while names of islands that use the form "eilean + [noun in the genitive case]" cannot take the definite article before eilean. Mhanainn is in the genitive case (the form that changes 'Man' to 'of Man'), and Gaelic noun phrases that use the genitive can only use the definite article for the last element (e.g. Pàrlamaid na h-Alba, not a' Phàrlamaid na h-Alba - the Parliament of Scotland, taghadh Pàrlamaid na h-Alba, not an taghadh na Pàrlamaid na h-Alba - the election of the Parliament of Scotland, (i.e. the Scottish Parliamentary election). In English, you need the definite article at the beginning of the phrase and for every element in it that would normally take one, in Gaelic only the last element gets the definite article. If, as in Eilean Mhanainn, the last element doesn't need a definite article, no element of the noun phrase gets one.
This should start to make sense once the genitive case comes into play in the course, but for the moment, it's probably best to recognise that the names of some islands need a definite article, and some don't, and just learn these as you go.
I would add that it is quite equivalent to English when it uses the ’s genitive. Let’s look for example at mac an fhir – the son of the man, or with the ’s genitive: the man’s son and not the man’s the son with the article repeated – the same happens in Gaelic when using the genitive.
The same way Eilean Mhanainn is literally Man’s Island (and cannot be Man’s the Island as that makes no sense).
In some cases one might mirror the use of English X of the… using the de, off, of preposition, but mostly in a partitive meaning, eg. fear de na bàird Ghàidhlig ‘one of the Gaelic poets’, beagan den chàise ‘some of the cheese’ – and it is not used so commonly as in English, and I don’t think it is ever used for definite phrases of the type the X of the Y.