Air carrier Captain reported an abrupt stop was necessary to avoid a collision while taxiing from the gate at DEN airport.

Narrative

We were pushed back from gate XX and Ground gave 2 aircraft taxi instructions from the north port east on taxiway Golf. Ground then cleared us to taxi east on Golf to Mike across 9R. Gate XX requires the 2 engine taxi out due to confined spaces; I executed a 90 degree turn and was perpendicular with taxiway Golf slowly creeping on to Golf due to the jet blast restrictions. I saw Aircraft Y just leaving the north port; we had plenty of space to get in front of them; however we were not moving quickly as to not blast the gate area we were vacating. The Aircraft Y picked up speed and looked like it wasn't going to give way or even saw us so I slowed down even more. They taxied past us completely unaware we were even turning out of the gate area. There was still a gap between the Aircraft Z; I was already well past the gate departure area and approaching the dashed line on Golf. The Aircraft Z also appeared not to see us entering the taxiway; still had nose light on and was picking up speed. I turned back to the right a bit and aggressively applied the brakes as it appeared they were not stopping or giving way. As they approached I couldn't tell from my vantage point if they would strike our nose with the wingtip. On ground I said 'Aircraft Y on Golf STOP'. They proceeded past us with maybe a foot to foot and half clearance. Once we were able to get moving again we taxied down Golf and followed our instructions to 9C/FF.