Not all that essential if your primary goal is directional audio for gaming. DACs don't have the kind of processing for that - for the most part even if you blow $6,000 on a Wadia DAC what it will do for that situation is not mess up a headphone audio signal that already has virtual surround processed in to give you directional cues, so really the DSP is more important.
Even if your games have built in headphone audio the DAC isn't all that necessary. You'll need it more if you want to be sure you're sending a clean 2V signal into an amp, and you only need the amp if you need more clean power to drive a headphone.
Given the headphones you listed as under consideration, any decent soundcard can drive those since they have high enough sensitivity to get loud without getting a lot of distortion for any distortion and noise to be noticeable when you're processing all other stimuli in games that have mp3 audio anyway. There can be some gains for music playback since (preferably) you're not distracted by anything,
but there's no guarantee that you can detect those differences especially if you don't sit back and just listen (ie you're browsing while listening). Even decent gaming motherboards can handle those Philips headphones well enough, just that some can have a high output impedance and it's hard to tell which one does unless you test it yourself (by contrast even soundcards that have a high output impedance tend to list it somewhere, just not prominently, like old pre-SB-X SoundBlasters).
If your games have built in headphone audio and your motherboard has a DSP and a decent driver circuit, and it sounds fine on the SHP9500S or X2HR (whichever you get), then no.
If you think you're losing because somebody has better DSP, I'm going to tell you no. If you want to try it out anyway, then sure, compare the native in-game headphone audio, motherboard DSP, and soundcard, pick what's best for you; if it doesn't make a difference to your fragging or you can't detect any difference to begin with, remember I said it wasn't essential.
If you get a headphone that has lower than 96dB/1mW sensitivity or higher than 250ohm impedance (or much lower than 32ohms) and you want to listen to music, then sure, there's a point to getting an amp along with a DAC-HPamp, whether you hook it up to your mobo (assuming it has a DSP that works on games, and not the bundled Realtek Dolby Headphone like on laptops that only works on movies).
Depends. Does your motherboard have a DSP and SPDIF?
That said, whether it does or not, upgrading to a motherboard with better VRMs and VRM heatsinks can have a bigger effect on your fragging assuming you have good CPU cooling overhead and can get even higher clocks than what you get now, since that increases your framerate. That assumes you're already on a 120hz or higher monitor.
Well if it only has USB then it won't matter if you get a soundcard or if your motherboard has DSP - using USB will bypass the DSP chip rendering it useless and you're stuck with the built-in headphone audio in your games (if they have them, although now that even Total War has it, I'd be surprised if there are still FPS games that don't).
OK...get this.
http://www.wadia.com/en-us/products/di322
Oh wait, over budget. Waaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaay overbudget.
If you want the absolute best surround experience ditch the headphones and work around having to walk around the rear satellites on these, making sure that they're all positioned equidistant to your head. Still overbudget but hey, it's real surround.
https://www.amazon.com/Logitech-Sur...10E5GPBPM8W&psc=1&refRID=9PXA4BBHR10E5GPBPM8W
X2HR. Tried the X2 and it has good enough imaging; judging by what people say about the SHP9500S, imaging size isn't that much of an improvement over Grado Prestige series.
Those can get loud enough without bad distortion that would be noticeable on games.
In terms of maxing out power ceiling and damping factor by making sure you have a low output impedance amp for music, well, those amps can help. Just that there's a chance you might not be able to hear much of a difference unless (or even if) you crank it up.
Honestly if you're willing to get a lot of equipment then just save up for a better DAC-HPamp for music and either get an Audio Technica ATH-AD900X for now, and if you don't like it get something else for music along with the DAC-HPamp later; or get an HD800S later and use it for both gaming and music (but maybe use a tube amplifier for it).