It would appear that your pet was on passive for almost the entire fight. Also you were using the felguard, which is fine for starting a fight, but you should be using the felhunter anyways. Your immolate uptime was very subpar as it should not fall off at all via Hand of Gul'dan. Your incinerate damage is WAY too high. You have 3 procs of molten core, which implies that you should only have 9 incinerates casted the entire fight. You casted 58 incinerates which is really blowing my mind, so that's 49 incinerates that did crap damage and had a long cast time. Your spec is not the incinerate spec, and you shouldn't use that spec anyways. You should only use incinerate during molten core. Use shadowbolt as your filler instead of incinerate. You only cast Hand of Gul'dan 13 times, and in that 5 minute time frame you probably should have casted somewhere closer to 20 (technically it should be much more than that if you do it properly). That would help explain why your immolate fell off so many times, and why you had to recast it 6 times.
The gaps in the green bar are direct DPS losses from poor immolate uptime. Immolate is a pretty big chunk of your damage as demonology.
The gaps in the second green bar are for shadowflame and reflect a dps loss because of the large gaps between them. In the middle of the fight it looked like you were using shadowflame on cooldown, which you should do, but at the beginning and end of the fight you were not. There's not much reason to slack there considering you're in melee range the entire fight and you don't have to move.
The biggest thing though is that you were using the wrong pet, and your pet, Veevazul, was only attacking for 67 seconds out of a 300 second fight.