Is it possible to use magic without saying "System Call" in Sword Art Online - Alicization?
In the case of Quinella, she had previously used a ritual (which did involve evoking "System Call") which gave her body a permanent barrier to defend against all metal weapons. The Kirito and Eugeo fight probably was the anime skipping over the initial line, possibly with some excuse about "whispering" the line.

However, there is more to the "magic" in UnderWorld.


   The Incarnating Arm that Eugeo used to retrieve his sword from Kirito is just one application to a very broad power. We've seen it portrayed in earlier episodes, but this world works on the power of imagination, Matrix-style, because of how all the Fluctlights in the Light Cube Cluster and Soul Translator are connected.
 The incarnating arms are just one way to use this. Incarnation as its called can also reproduce the effects of System Calls, but this requires a particularly powerful imagination.


You'll see a lot more examples of this in the 3rd and 4th cours of Alicization (once that point is reached)