ZSE Controller reported military aircraft was off filed departure route and entered a higher MVA resulting in a CFTT event.

Narrative

Aircraft X called on the ground at EAT looking for IFR clearance to EAT (via a long training route). I cleared the aircraft as filed at the requested altitude; 7000; which was safe for the route of flight until at least ZSE Approach Control's airspace (ZZZ sector). I instructed the aircraft to contact me leaving 4000. When they did; I noticed that they were southbound entering the 8600 MIA. I queried them a couple of times if they were flying some sort of departure procedure and they indicated that they were southbound towards ELN. I said that they needed to be on their filed route towards QUINT; and they indicated they were turning that way. I and gave them a low altitude alert (admittedly probably a bit too late and with imperfect phraseology) and climbed them to the MIA (8600). There was other traffic at 8600 so climbed them to 9600 and vectored them to the south (H160) to avoid a traffic situation. Once above the MIA; I instructed Aircraft X to climb to 100 and fly H065 to keep him clear of traffic. I asked Aircraft X his intentions. He said he wanted to go to ZZZ and get vectors for ILSXX. I gave him a southerly heading and handed him off to ZZZ1 [Tower] after explaining why I wasn't comfortable clearing the aircraft on course. The relieving controller read the Brasher statement to Aircraft X. Suggestion: I could have assigned the OFARO SID to the aircraft which would have been another way to reinforce the aircraft going eastbound on departure; although I don't know if that would have made a difference. I am still not sure why the aircraft decided not to fly its filed route.I was really startled by this situation; especially considering that I had traffic at the MIA; and am disappointed that I reacted more slowly than I would have liked. I was pretty flustered. Some of my actions were too slow and others were too excessive.We were on the standby for CHXX and it didn't seem to be working as well as the mains. Having to repeat transmissions added a bit of complexity to this situation.