"I do not like this game."
Translation:Мне не нравится эта игра.
Words order in russian languange is a separate big topic and I'm not sure that I can find out some strict rules here. I'll try to explain with that particular example
'Я не люблю эту игру' - I don't like this game. 'Я эту игру не люблю' - Also correct, but.. It's more for the context where someone suggests to play that game and you reply 'Я эту игру не люблю'. Or if you tells someone about that game and in the end you say '..' like a resume 'Я игру эту не люблю' - still acceptable, closer to the second option 'Эту игру я не люблю' - I don't like that particular game. But I'm ready to play other games 'Игру эту я не люблю' - still acceptable, but I would expect to see the sentence before with the word 'Игра'. 'Игра предполагает избивать людей. Игру эту я не люблю' - Game supposes to beat people. I don't like this game'. But this is more book-style
So.. There are many ways how you can place words, some of them correct, some of them not, some of them give you a bit different meaning.
There is no way in english language to define russians cases I don't like this game can be translated as Я не люблю эту игру Or Мне не нравится эта игра
So there are some rules already in russian language, english sentence itself doesn't give you the information about the case