Air carrier Captain reported while waiting for takeoff another aircraft proceeded across a non movement area and cut in front of the Captain's aircraft.

Narrative

I was Captain and Pilot Monitoring for Aircraft X from ZZZ to ZZZ1. We were holding short of the ILS critical area at the approach end of RWY XX in ZZZ waiting for our take off clearance for our wheels up time of XA:23. We were holding short of the ILS critical area due to construction equipment cleaning FOD on Taxiway 1 in the ILS critical area. The FOD was cleared and tower cleared us to take off. As I started to roll forward Aircraft Y taxied very closely past us on the left side using the non-movement area line as a taxi line. As soon as I saw the aircraft in my peripheral vision; I stopped my aircraft and Aircraft Y then stopped ahead of me to the left. I did not feel comfortable with the wingtip clearance to get passed Aircraft Y so our take off clearance was cancelled and Aircraft Y was given number 1 for takeoff. Due to this we missed our XA:23 departure window and were given a 19 minute delay for a XA:42 departure. I informed tower that I would file a report before the other aircraft left tower frequency due to the close proximity of the wingtips as they passed us.Suggestions: Aircraft Y pilot should understand the difference between a taxi line and a nonmovement area line and understand that they cant cut to the front by cutting off an aircraft who has an active takeoff clearance.