Air carrier Captain reported executing a low altitude go-around at LGA when another aircraft taxied onto their landing runway.

Narrative

While on approach ILS to Runway 4 in LGA Aircraft X which I thought was going to stop while on a crossing taxiway continued across the runway. At that time; my attention was truly focused on him. At approximately 200 feet he was taking his time and I initiated hand flown go around. The only call the First Officer (FO) the non flying pilot missed was positive rate. With the Tower now giving us instructions quickly it interrupted our standard calls. I don't recall if I asked for flaps two first or the gear regardless the gear came up first and then the FO went immediately to flaps 2. We received only one oral warning. During climb out once again it was hand flown and VMC so I was heads up the entire go around. I believe I missed the heading call because Tower was still giving us instructions. At 1000 ft. I asked for Flight Level Change (FLCH) speed 210 and heading which the FO performed. I saw the FO hit FLCH yet once again I was more focused on airspeed I didn't notice for some reason we ended up in FPA. After cleaning up we entered the downwind and landed Runway 4 with no further incident.