Other examples of this structure or form.
- He saw the man leave.
- They heard the door bang.
- She felt her pulse race.
- We watched the house burn.
- I listened to the music play.
- He looked at the squirrel run.
- We experienced the situation worsen.
- I perceived the the bell ring.
- We noticed the door open.
So, those are some of the verbs that can work this way. They all involve having a direct experience of some thing.
If you take the direct object and replace the present simple verb with when it + the verb, the meaning is clear.
- I saw the man leave. = I saw the man when he left.
- They heard the door bang. = They heard the door when it banged.
The examples above where the third person plural s is not used, are just like:
- We suggest you leave.
- I recommend he go.
- It is important he play today.
However, in the first group of examples, the main verbs are all in the simple past. Except for stage or movie script directions, the simple present here would be odd, though the continuous would not:
- He sees the man leave. [theatrical script]
- He saw the man leave. [real life]
- I'm seeing the man leave. [real life, as he leaves]
This used to be called subjunctive in English. Many linguists would call this a bare infinitive today.
Personally, I would argue that these examples parse like this:
And that "the man leave" is simply a direct object phrase in the form of a subject plus bare infinitive as with verbs like recommend or advise or suggest.
Same as: I watched//the balloon rise.
These can also be analyzed as noun clauses:
For example, from the linked text:
The sales clerk suggested she put the dress on hold.
To summarize, some verbs of observing and experiencing function in a way similar to the verbs advise, recommend and suggest where the noun phrase verb in the third person singular does not take an s.