Translation:It is three o'clock.
Correct. Not just in time, but counter words in general always need to be included. As a non-native speaker, natives will give you a lot of room to make errors as long as the number is right.
Also about that assumed information. In english "do you drink" and "飲みますか" have a completely different implied meanings. In English we assume alcohol, in Japanese its like "Of course i drink. Water, coffee, tea, etc."
And to add onto this as to what context would make you use one over the other:
You would generally say "It is two o'clock right now" just when giving the current time because you are referring to the time at that moment.
Whereas say you were telling a story about someone's day and you are telling it in the present tense as if narrating it. You would say things like "it is two o'clock, john leaves for his lunch break " and have no mention of "right now" because you are not referring to the current moment in time, you are just giving a time of an event. Or if someone asks you what time the party is at later, you would simply say "it is (at) two o'clock" with that phrase
I think the usage is not much different from English. You use "right now" only when you are stating the time at that moment. If someone asks what time it is (now), you can respond with either "２時です。", "今、２時です。" or "今は２時です。" When you tell a story, normally the sentences take the past tense, don't they? In this case, adding "今" would be strange and unnatural. Your example with John is to explain his usual habit or routine, I think. The literal translation "２時です。ジョンはランチに行きます。" would sound a little awkward. I would say either "２時にジョンはランチに行きます。", "今、２時です(から)、ジョンがランチに行く時間です。”, or "ジョンがランチに行くのは２時です。” Lastly if someone asks you what time the party is at later, we simply say "２時です。" Does this help you at all?
In the tiles for o'clock they have incorrectly placed the apostrophe with "clock". If they insist on separating it into two tiles, the apostrophe belongs with "o" because the contraction is for "of the clock" and what's removed was taken from the "o", not "clock".
They got " You / 're " right. Why did they mess up on this? Did they not know it's a contraction? It has an apostrophe; they should have been able to figure that out.