Hello dear friends,
I witnessed an interesting usage of Present Simple which I would like you to explain. To cut a long story shorter I will say there were a group of people walking back to a building where they were staying. One of them went forward and reached the door before the rest of them and started waiting. Approaching this guy another member of the group exclaimed - He meets us at the gate!
The speaker was american and I quite believe that it was a well- considered exclamation.
So he used PRESENT SIMPLE in order to express an action which was quite temporary and limited withith a short period of time. The official position as for the Present Simple is that it doesn't express short actions limited by a certain time frame rather then Present Continuous fits better fir this situation.
Wasn't is better to say - He is meeting us at the gate?

What are your thoughts about it?
Reagrds
There are about 6 uses of the Present Tense, and you are probably aware of one, where you might also expect the Present Continuous - live commentaries on radio and TV.

Rogers kicks the ball to Hargreaves, who fumbles the catch and Liverpool take control...Collins has the ball and ...kicks...it's a goal for Liverpool!

There is another which I think pertains more to your example, called Declarative Style - as if the speaker is making a formal announcement about something.
- a servant rushes in and wakes the King. "Sire, the barbarians storm the castle!"
to storm: to make a direct assault by troops on a fortified place.

In your anecdote, the man is probably being humorous. Perhaps something about the situation reminded him of situation depicted in Classical literature, or history, and he phrases his observation to change it from being just a routine, mundane action, to something momentous!

Say, two friends had a falling out, and one wants to make up, but the other is adamant he will never speak to the person again. I throw a party, inviting both. The 'adamant' friend refuses, because the friend he now hates is going to be there.
The party is in full swing, when who appears at the door with a 6 pack in hand....
I see him from across the room and I whisper to another friend, "Behold, the Mountain comes to Mohammed."