Learn English – Which of these sentences is correct: “Our topic for today is games.” or “Our topic for today is about games.”

The form I have encountered is:- He plays games on his laptop. I don't particularly know why - it just seems idiomatic.

Of the three versions you have suggested, the first sounds wrong, as it suggests he is inside his computer. I would argue that the second and third are both correct, though the third has a subtle difference in meaning.

At first none of the examples sounded good to my ear, but after I looked it up it seems that the 2nd and the 3rd are correct.

1. Many discuss the topic that whether medicine has true benefit on our society.

Whether is a subordinating conjunction. That is also a conjunction. Pilling up conjunctions one after another does not serve a purpose, and it is grammatically incorrect. Both of these conjunctions can be used to introduce a noun clause, but in your example the noun clause is derived form a yes/no question:

Does medicine have true benefit on our society?

Therefore you should use whether (that is used for noun clauses derived from statements).

2. Many discuss the topic of whether medicine has true benefit on our society.

Google books shows evidence of "... of whether..." construction usage, e.g. in: "...the question of whether the pure self can be conceived of in unity with a living organism." At the same time LDOCE gives examples of the construction "topic of". Since these two were my main concerns, the sentence should be correct.

3. Many discuss the topic on whether medicine has true benefit on our society.

Again, there is evidence of usage of the phrase: topic on whether, although there are only 68 hits, which would indicate that this phrase is used rarely.

Finally, Many question whether medicine brings a true benefit to the society would be my personal preference, but there are many ways to phrase this thought.