ZAB Controller reported miscommunication of routing verification of release by flight data resulted in traffic and restricted airspace conflict.

Narrative

While working Sector 17 and at approximately XA11 zulu time; I received a call from Flight Data requesting release on Aircraft X from the Gallup; NM Airport (GUP) to ZZZ Airport. I cleared Aircraft X from GUP airport to ZZZ airport as filed; clarifying via Victor 60 with a departure altitude of 13;000. In the meantime; Aircaft Y was given a clearance from FL220 to 10;000 landing at GUP. When Aircraft X called airborne I stopped the climb at 9;000 to separate from Aircaft Y by 1;000 ft. Aircraft X then proceeded to turn SE bound on V291 instead of East on V60. This put him in confliction with the Ft Wingate restricted area of surface to 11;000 ft. I immediately climbed Aircraft X to 13;000 ft to avoid the restricted area. This put him in confliction with Aircaft Y. Loss of separation did occur at the same altitude and approximately 4 miles. I asked the pilot of Aircraft X what his clearance was; he stated it was as filed; V291. The flight plan in our system showed the filed routing to be GUP. V60.ZZZ.ZZZ. Recommendation: I believe it would be good practice to read a full clearance instead of saying 'as filed'. I did this during the call with Flight Data; saying; 'Cleared as filed; I'm showing V60 to ZZZ.' This would take any confusion away from the pilot; FD or the Controller. I am unaware what the clearance given to the Pilot was.