Air carrier Captain reported they were stopped at their assigned spot on the ramp when they observed another aircraft taxiing towards them that did not stop '...until the last minute.'

Narrative

After landing on XXR; we got off runway Tower told us to turn right on Taxiway 1 for Taxiway 2 and contact Ramp. We turned right on Taxiway 1 to Taxiway 2 and contacted Ramp 1 where they told us to taxi via Taxiway 2 and hold short of Taxiway 3 at Spot X at Taxiway 4 to allow an aircraft off our left side to go by. I decided to stay facing east since there was not much room to turn to be perpendicular and hold short of Taxiway 3. Next thing we see the aircraft we were told to reference heading eastbound on Taxiway 3 and they started turning right onto Spot X and right on Taxiway 4. This was Aircraft Y and they were talking to Ground. ZZZ procedure is to talk to Ground going out and Ramp coming in. Aircraft Y kept coming and did not see us parked there until last minute. I jumped on Ramp and asked what they were doing. Ramp did not know since Aircraft Y was talking to Ground. They saw us last minute. You could see that the right seat Pilot FO (First Officer) did not clear all the way to the right until last second and they finally and quickly stopped when they saw us. It was tight but I was able to get past them and recommended to ramp I continue east on Taxiway 2 up to Spot Y. First; Ramp and Ground did not properly coordinate who was going where. Second; FO in Aircraft Y did not clear their aircraft as far right as he could see until last second. Proper coordination between Ramp and Ground controllers. Proper clearing of an aircraft when turning on taxiways.