After studying the Cambridge Grammar of English a little bit, my perspective on this question has changed, in a way that I must say I find pretty elucidating.
In the CGEL - in many grammatical dimensions, such as clause type vs. communicative function - it is heavily stressed how often there is a difference between grammatical form vs. semantic meaning. In fact, we are so used to hearing grammatical forms defined in terms of, or as having, a specific semantic use; that is (apparently) what defines them. For example, the “preterite” in English (we are told) refers to the past tense. This appears to be so widespread that it may be disorienting and hard to grasp when one first considers the idea that the preterite has no meaning in and of itself. The preterite is (according to the CGEL) only a shape, like looking at keys and saying this is a skeleton key, this a bump key, and not (yet) saying anything about where they can be used (the lock on the front door, the lock on the shed, etc.). Later, you define certain rules/structures/clauses, which do have a semantic meaning, and which call for a certain form. But one can observe sentences in which the preterite form means past, present, or future (in the latter, “You said it started tomorrow.”
It seems like meaning controls form more than form controlling meaning, but that’s my thought, not sure if guaranteed.
The parallel with tense is that while all languages can obviously communicate about states of affairs which necessarily happen to have occurred at a certain point in time (past, present, or future), I think (according to the general view on grammar taken by the CGEL’s authors), the question is not about what languages can communicate, but only a question of what time-related grammatical forms the language has. What I found surprising but definitely memorable was the authors’ claim that, actually, English has no future tense. If you look at the grammatical behavior of a word like “will”, the authors’ argue that it behaves like a modal auxiliary (words like can, might). It also seems to have more variegated meaning than is often relayed in grammar lessons. The authors say that “will” is associated with dynamic modality - a way of talking about what someone is able or willing to do, along with words like can.
I find this refreshing. It seems that the verb “will” indeed often conveys one’s will (in the sense of volition), for example, in the sentence I asked John to fix it but he won’t. Bringing back the connection to Chinese, I am pretty sure the Mandarin word hui similarly can mean roughly “can” or “will”, depending on context.
In the CGEL, it’s stated that English has 2 tense-related forms - present vs. preterite (run vs. ran), and perfect vs. imperfect (run vs. have run).
How I understand this to bear on the question and some of the answers above is that it may not be the case that languages are so strictly time-marking or not - according to the analysis above, English is nowhere near as time-marking as I originally claimed it was; and a language like Chinese has ways of implying time that are actually similar to at least some English constructs. For example, I said that Chinese can use the present form to refer to the semantic future - but this is not actually distinctive to Chinese. I know this to at least occur in Germanic languages such as German and Swedish. Furthermore, it can even occur in English: Tomorrow, we ride. / You didn’t pack? We leave tomorrow!
Although I don’t know Chinese well, one might inquire into whether, since Chinese I think is an “analytic” (high morpheme-to-word ratio) language, that Chinese can’t denote tense through inflection - since it doesn’t have inflection. This is a very trivial characteristic which we should not take to imply “there are no tense markers in Chinese”. English (according to the CGEL) has a tense system marked by a separated word (“have”). In principle, it’s perfectly possible the same is true in Chinese.
This is a satisfying development on my perspective on this question, some time later!