Learn Portuguese (Portugal): Este livro é útil para ele, mas não para mim. - This book is useful to him, but not to me.

Because it comes after a preposition (para). In Portuguese, prepositions must be followed by special 'stressed' pronouns. For the first person, the subject eu (I) changes to mim (me) after words like para, de, or sem. You cannot use me here, because me is an object pronoun used directly attached to verbs, not prepositions.

If eu changes to mim, why doesn't ele change? Isn't ele just 'he'?

That is a great shortcut in Portuguese! Only 'I' (eu becomes mim) and the informal 'you' (tu becomes ti) change their forms after prepositions. For the third person, ele is used for both the subject ('he') and after a preposition ('him').

The English translation says 'useful to him', but doesn't para mean 'for'?

Yes, para usually translates as 'for'. In Portuguese, you describe things as being 'useful for someone' (útil para ele). The translation says 'useful to him' simply because that often sounds more natural in English, but the Portuguese literal logic uses 'for'.

A quick refresher: why is it este livro and not esse livro?