Okay, first off - it's cool that you ask stuff like that. Aion-players aren't usually interested in improvement...
Second; gear is important, but it's not everything. A lot of people think two equally geared players would do equal damage, which is FAR from being true though. Keep that in mind.
Looking at your specific case, I guess the other ranger was simply killing Ides without doing any mob- or boss-damage. So he used his 'best' skills to burst the Ides and then kept waiting for them to respawn. This way he had a high DPS in the time he actually did damage and the DPS didn't drop afterwards by the use of the 'worse' skills, because, well, he didn't use them... The time in which a player doesn't do any hits isn't counted by the DPSmeter. But recorded DPS isn't important anyway. Just ignore it and look at the overall damage.
So... Why's your damage on Hyperion so low?
Maybe you were the only one who did damage on the adds while everyone else kept dpsing the boss. Could be. I don't know. But boss-damage is worthless anyway, so let's skip that.
Let's get to your overall damage. I guess that's the 1.2mil you are talking about.
If the Ide-killer also did the same amount of damage, I guess the duration of your run was about 13 minutes. This means your actual dps is about 1,500. That's quite bad to be honest.
This could have several reasons. Maybe you aren't weaving properly. Maybe your stigma-build isn't optimized. Maybe you aren't using your buffs properly. Maybe you don't even have your important damage-buffs because your stigma-build sucks, idk. Maybe you are constantly idling instead of pressing some skills... Could be anything.
What I do know: Your stats are a little bit off.
1150 crit strike is okay, but you'd be capped at 1200, so why not just get there? 921 crit without any sort of buffs is the value to get to. Then you add a scroll (120), food (60), an idian (at least 34) and chanter's intensity mantra (65), which then equals to 1200. Add 65 crit if you want to always be capped without a chanter.
Your accuracy is too high. That's not bad or anything but you are wasting slots. 2500 is enough to hit Hyperion and 2800 to hit all the adds. But you'd need more for Dynatoum, Grendal and Sheba, so just stick to about 3000.
I don't know how much attack you have, but you should push it as high as possible, since it DOES increase the damage caused by skills.
Also, the dps-wise best stigma-build is this one: http://aion.aspirine.su/stigma/#eCnaaadeBkehaBmaBdhsguazfigBlaBia
I'm not saying you should use this exact build, but you should try to get there as much as possible.
If I would see your gear, stigmas and gameplay, I could say what's right and what's wrong, but this is all I can currently help with.