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Physics is amazing
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Correct, the net downward force stays the same (minus the weight of the matchstick).
But the net force isn't really important, the important variable is torque. Torque is force at a distance that causes rotation, if the match rotates it will free the bottle and fall.
With the addition matches, there is now a small upward force on the tip of the match that doesn't affect the net force because of an equivalent downward force on the match near the edge of the table.
However because that small upward force is much farther from the edge of the table (the matches pivot point) it's able to bring the torque on the match into balance and keep it from rotating.