Air carrier Captain reported while lined up on taxiway; they had a ground conflict with another aircraft on the same taxiway.

Narrative

At approximately XA:05 we received a taxi instructions from ground to cross 22 at papa and follow Aircraft Y on gulf.; we read back the instructions and were then given 'follow Aircraft Y infront of us to 13; and monitor Tower'. We were number 3 waiting in line. While in line Aircraft Y; asked the Tower for a sequence. They were told they were number 2; but there were already 2 other aircraft infront of them. At approximately XA:10 they were told to standby by the LGA Tower. The line on papa was progressing towards the runway; each aircraft turning on their taxi light as they stopped and started; at the same time Aircraft Y was slowly taxing into the line of aircraft on papa. We were unaware they were moving because it was 1/4 mile visibility and they were not using any lighting to indicate they were moving. At approximately XA:11; Over the Tower frequency a voice came on and said 'stop; stop'. It was the Aircraft Y. Tower was unaware of what was happening and I came on to advise them how close they were to us and I believed we were unable to move; Aircraft Y advised Tower they could get passed us and they accepted a line up and wait. I called the LGA Tower after we landed in ZZZ to report what had happened.