All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
In principle all games are permissible unless they lead to abandoning an obligation – such as abandoning the prayers – or committing a prohibition – such as gambling, like playing for prizes, or if it involves revealing the ‘Awrah and so forth. The Fatwa of the Standing Committee reads:
"Football matches that are played for money and similar prizes are forbidden, because it is gambling. It is not permissible to take a prize except in things that the Sharee‘ah has deemed permissible, namely racing horses and camels, and competing in archery. Nonetheless, if the match is not for a prize and does not prevent one from performing something which Allah has enjoined, such as prayer and the like, and it does not involve anything that is contrary to the Sharee‘ah, such as uncovering ‘Awrahs, mixing of men and women, or musical instruments, then there is nothing wrong with that or with watching it." [End of quote]
As for wearing T-shirts that have an advertisement for a company that fosters Muslim and non-Muslim children, then there is nothing that requires its prohibition.
As regards the company that produces trophies in the form of images of living beings, the fact that there is an advertisement for it in a site does not necessitate the prohibition of entering such a site and surfing it, as one would not be promoting the company by doing so, nor would it be a direct help for its activity.
Also, the fact that the company sponsors the association responsible for organizing the game does not make it prohibited to play the game.
Allah knows best.