Also, neither statement has a clear meaning because it’s not obvious what ‘making the most of the Olympics’ means.

The first sentence is grammatical but makes little sense. "Appears" is present tense but "next year's game" is in the future. How can a future event "appear" to you? It would make sense if you said: "China appears to be making the most of the approach of..." or "China is planning to make the most..." or "China wants to make the most...". "Set to" also means "able". So it means "ready, intent, and able". Ability is an important part of the meaning. You don't say someone is "set to" do something unless you think it is likely to happen.

I think it may be treated as plural in English, because at the olympics there are many plural games happening at once. In one overall over arching competition of many games played on plural fields and venues. That include all manner of sports using venues sports fields/pitches/courts/rings. It was the Olympic Games since its inception from the greeks many years ago.

I agree with Robert. Also, it's OLYMPICS or OLYMPIC GAMES, not OLYMPIC GAME. For some reason it's treated as plural in English.

Sentence one, China appears to make the most of next year's Olympic Game. does not make sense compare: China wants (NOW) (present verb wants) (something in the future) to make the most of next year's Olympic Game. Sentence two, China appears set to make the most of next year's Olympic Game. China appears set (or ready) (NOW) (present verb appears) (an action in the future) to make the most of next year's Olympic Game. Note: to appear takes an adjective, not a noun he appears fat he appears lazy he appears angry etc. set is an adjective, often followed by "to do something", like sentence 2 or example: the old man is set in his ways. Here set = established, rigid or the dinner table is set. set = ready, prepared are you all set for the exam.