I am almost certain that, in that situation, the Lord's voice was a physical acoustic phenomenon. There is nothing preventing the Lord from interacting in the physical world. He isn't limited to a spiritual dimension only, any more than we are. If he were only going to interact with us through a still small voice and subtle miracles, why did he give us physical bodies and a universe full of energy, matter, and supernovas?
Jesus multiplied physical bread and physical fish. Angels moved a physical stone, and Christ took up again a physical body and told thousands of people to touch it.
I sometimes wonder why we want to focus so much on the spiritual sometimes, that we forget the value and reality of the physical. (I actually have a theory based on some psychological personality theories, but that's besides the point.) It is important that we don't view the Lord as limited in his ability to interact with us.
Perhaps this scripture will help in interpretation. It's Nephi speaking to his brothers later on, probably referring to the original quote.
1 Nephi 17:45 Ye are swift to do iniquity but slow to remember the Lord your God. Ye have seen an angel, and he spake unto you; yea, ye have heard his voice from time to time; and he hath spoken unto you in a still small voice, but ye were past feeling, that ye could not feel his words; wherefore, he has spoken unto you like unto the voice of thunder, which did cause the earth to shake as if it were to divide asunder.