Air taxi Captain reported a critical ground conflict with another aircraft while exiting the runway. Captain brought the aircraft to a stop and notified ATC.

Narrative

On Day 0 my FO and I just landed at BWI XA:14. When we exist the runway from 33L to taxiway Romeo; from there tower told us to contact ground. While the FO was trying to call for taxi clearance there was a Aircraft Y taxing on taxiway Papa. When I existed the runway of course I have to clear my entire aircraft past the boundary lines. My nose was pretty much already taking up a little bit of Papa. Aircraft Y without hesitation kept going even though there's not that much space. I don't think he saw me because I had my lights off when I was at a complete stop. I tried to get his attention by turning on my lights but he still didn't care to stop and just kept going. Ground did ask if we had space to get in front of Aircraft Y which by the time we replied we couldn't make a sharp of enough turn to clear him. Aircraft Y did have move left of center line just so we had enough space. At the end he did get in front of us and risked his winglet almost colliding with our fuselage. I understand that ATC did not tell him to stop and allow us to past but that was huge risk where we could've hit each other. I was unable get his flight number; he was departing from BWI though. We then continued to taxi with no other issues (Papa; Kilo; cross 33R into the ramp).