There is a difference between pedantry and idiomatic usage. At the end of the day (and this particular answer), I'm judging this based on two people communicating an idea and what is commonly understood, not some microscopic rulebook grammar.
0 - [You may do x] when you see a creature within 60 feet of you casting a spell
Pedantically, this means you see both a creature and its spellcasting activity.
Let's consider the case where they meant that you see the creature, and that the creature is casting a spell, but there is no requirement for you to see the casting itself. How would they have needed to phrase that?
1 - [You may do x] when you see a creature within 60 feet of you which is casting a spell
This resolves the issue. You see a creature. Specifically, a creature which is casting a spell. It does not state that you see the casting itself.
2 - [You may do x] when you see a creature casting a spell within 60 feet of you
Doesn't fix it. Pedantically, it still means that you see the casting.
3 - [You may do x] when you see a creature which is casting a spell within 60 feet of you
This resolves the issue at hand. However, it makes an unintended suggestion of maybe meaning "casting [a spell within 60 feet of you]", which I could interpret as measuring the distance between me and the target of the spell, e.g. if the creature were casting a fireball with the intention of hurling it at me.
That's not necessarily the correct reading, or the only correct reading; but it is an annoying additional point of confusion.
The same potential misreading applies to option 2, but this option was already rejected for other reasons.
"which is" resolved the issue here in both cases 1 and 3. It decouples what you see from the act of spellcasting, instead only conveying that you see a creature and that this creature is casting a spell.
However, I do consider that context applies here, and people are liable to understand the same information from all of these examples. Pedantical grammatical differences aside, you're going to find that people will regularly omit things like "which is" in their speech and completely ignore that this may create a nuanced difference in interpretation.
I also want to take the time here to point out that I can very easily start picking at any thread I want here:
- What if I see a creature casting a spell, but I'm looking at a camera monitor?
- Must the monitor be within 60 feet of me?
- What if I see the creature via the monitor, but the creature is in reality still within 60 feet of me as well, just not directly visible?
- What about a mirror?
- What about looking through an open portal?
- What about me being blinded or visually impaired, but I have someone explain to me very clearly what I should be seeing?
- Does "seeing" limit the rule to eyesight?
- What about blindsight?
- What about darkvision?
- Can a creature (or their ally) cancel your ability by interrupting your line of sight for a brief moment; even though you've already seen the creature (and its casting) and know exactly where it is?
- Suppose you are hallucinating, and every fiber of your being believes that it is seeing a creature and that it's casting a spell. Does this somehow unlock you using your ability?
- What if the creature is real and you genuinely believe you've seen it casting a spell, but you're wrong?
- What if the creature is real and you genuinely believe it's casting a spell, but you've not claimed to have seen it?
- What if there is a creature, and it is casting a spell, and you have seen the casting, and you've for great eyesight but are also a really bad judge of distance and it's just a bit further away?
- What if you're seeing a creature and spellcasting, but the casting is being done by a different creature than the one you're seeing? (e.g. it's not a dragon breathing fire, it's a dragon with a tiny fire mage in its mouth, and the mage is casing a cone of fire)
Your concern about seeing the casting itself fits neatly in this list in terms of how it picks at the threads of the rule. I admit that my examples are decidedly more pedantic, but it's the same principle at play.
I think it's unproductive to read the rules in such a definitively declarative way that picks at threads like this. DnD's rules are famously and frequently ruled in a way that gives leeway to the DM and the context in which a particular interpretation takes place, and the onus is not put on the rulewriters to write legalese in order to make sure that all possible edge cases are covered.
The significant addition of complexity and boringness to the writing would disproportionately detract from the fun of the game, turning it into a fantasy legal dispute.
Four relevant points to consider in order to answer your question:
- Pedantically, you are correct that the current phrasing means that you must see some evidence of spellcasting
- Informally, this distinction is not made and it will generally be understood to also include cases where you only see the creature, not its spellcasting
- When the two significantly conflict, we should judge language by how people understand it over grammaticality. I concede that this is my opinion on the matter.
- For DnD specifically, it is well established that there is leeway in these kinds of interpretations and that it should be ruled on a contextual basis by the DM in question. It has been historically acknowledged that there is a deviation from grammatical precision where it starts conflicting with fun, i.e. the primary goal of DnD.
Therefore, my opinion on the third bullet point aside, it seems fair to conclude that both interpretations are possible and can be considered valid for the purposes of a DnD rule.