I think it's correct too. According to Oxford ( http://oxforddictionaries.com/definition/english/gain?q=gain ): - obtain or secure (something wanted or desirable)
So "he will gain" should be accepted as correct.
You "could" say gain, but I do not think any native speaker of English "would" say it. The idea of (win) is to get something for nothing, so this sentence conveys the idea of winning a contest. If it were not a prize in a contest, then I would say, (He will take the trip of his dreams). Espero poder-lhes ajudado. Peduzzi e Paulenrique, gosto dos seus comentarios, ambos tenham-me ajudado no aprendizagem.
Wesley, esta é a primeria vez em ler algum coisa de você para mim. Um prazer. Como sempre, por favor, sentam com libertade em corrigir meus erros. Obrigado. Bon estudos.
Cambridge dictionary lists travel also as a noun: http://dictionary.cambridge.org/dictionary/english/travel
Maybe it has a different meaning or usage, since their examples lack articles. Thank you, anyway.
One of the major differences between English and other languages is that in English the possessive article accords with the owner or owners of something.
- He washes his car.
- They wash their car.
In Portuguese and many other languages, it accords with the object.
- Ele limpa seu carro.
Which can be, He washes his car, their car or your car, depending on context.
In the case of this example dos seus sonhos, it's most likely his dreams, but could be your dreams, or their dreams. Only context will give the true answer.