Word or phrase to describe banging finger downwards to demand something

One word I think you can use is gesticulate:

to move your hands and arms about in order to attract attention or make somebody understand what you are saying

He gesticulated wildly at the clock.

She was shouting and gesticulating from the other side of the road.

So you could say that someone was gesticulating at the floor to indicate his impatience.

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Another option is to use stab:

To make a thrusting or poking motion at or into: stabbed the air with his fingers.

So you can say that someone stabbed the desk with his finger, possibly also saying that he is impatiently doing so. If there is no desk, he stabbed downward with his finger.

The most common phrase for this is "banging the table", or "to bang the table".

If he's doing that on a Bible, you could say Bible-thumping. It's quite a common phrase, so you could expand that to '...he thumps his finger on the table...'