They would've lost at Vraks if space marines (4 different chapters of them) hadn't intervened several times to take important locations and defeat important enemies before leaving to do stuff they considered more important*, not to mention the Inquisition and 22 titans by the end of the war. Indeed, prior to the arrival of the titans and some new regiments as part of a reinforcement wave with a new commander in charge the war was lost, the DK already deployed were cut off, being systematically destroyed and generally just knackered.
Half lies, half misdirection. While in fact DK did have a major problem in the middle of the war, it was due to the arrival of very big CSM forces with Chaos Titans of their own. The forces deployed from orbit and have went around the Krieg trenches. Before the traitors received four CSM Warbands and a Traitor Legio of Titans of reinforcements, Krieg was winning the war. Shortly after a relief force arrived with more Korpsmen and regained the initiative. This is like saying "well the enemy suddenly got overwhelming numbers so Krieg of course lost the war if not for, well, more Krieg apparently.
Honestly I would probably have taken the Armageddon Steel Legion over the Death Korps for Vraks, though I do prefer the DK aesthetic their tactics are less than stellar even for their supposed speciality given the gear available. The main weakness the DK assaults had was improper use of armour and slow movement speed, as well as an aversion to actual thinking. The Steel Legion uses Chimeras which are fast and heavily armed with good frontal armour and an enclosed compartment, while the DK prefer Gorgon Transports, which are slower and open topped even if more heavily armoured and able to carry more men at a time. Really an open topped transport is a weird thing in general, especially when you still need a door to deploy from it.
But... Korps also use Chimeras? Heck, their Chimeras are generally upgraded to be better armoured and armed. Sure, they have more reliance on Gorgons, since they are the actually best thing to use in case of trench warfare. I'm not sure about the open-toppness of it, but I hardly see a problem with it. Sure, an artillery shell will kill the dudes inside, but they'd have to be unlucky, and at the same time most would go through armor on top too, and it's not like the doctrine doesn't call for artillery shelling of enemy positions anyway - in which case the enemy artillery is presumably suppressed and unable to shoot back.
A rapid massed mechanised assault of Chimeras and Hellhounds could easily burn out the outer defensive trench lines and better protects the infantry from artillery fire than the gorgon, as well as better able to follow and support disembarked infantry in most terrain. Chimera's are also amphibious vehicles, well suited to function in the muddy terrain of Vraks. I'd probably want some Elysian Drop Troops regiments in a perfect world, but I think Vraks was ill suited to most fliers due to the electrical storms, the DK didn't bring fliers any in any case.
Gorgons also have guns, and they carry a whole lot more guardsmen than Chimeras. The problem here is that while Chimera is really commonplace and cheap, Korpsmen are still vastly cheaper. For the same amount of vehicles you can deliver a higher number of soldiers into enemy trenches, and more soldiers means more flashlight fire to drown out the enemy. DK didin't bring fliers because they are an Imperial Guard regiment. Most Imperial Guard regiments do not own their own fliers (apart from Valkyries and the like, which are more like helicopters in terms of how they're used). Vraks in fact had bunch of aerial combat done by Imperial Navy air force though.
Of course this is a battle where Death Korps regiments tried to retreat. Some even shot their own Commissars for trying to stop the retreat, so I'm not sure any guard force could do it without problems, but I do think some could have made far better progress at it while also being more resistant to the traitor's main arsenal of artillery and massed small arms fire.
Krieg was ordered to retreat and they were shooting Commissars telling them to. Hell, even if they wanted to, they wouldn't be able to, considering the encirclement. A lot of them were still rescued by the relief force consisting of, surprisingly, even more Korpsmen and a bunch of Titans, though traitors had their own.
Granted the DK are somewhat better suited to resist chemical warfare than the Steel Legion, but considering that the chemical weapon that was stockpiled on Vraks literally melted DK soldiers into skeletons through their jackets and respirators I'm not sure being better at it matters much. Liquified is liquified after all.
Not all chemical (and biological, and whatnot) warfare is made equal. The stocks of the chemicals that killed them despite their protection were somewhat limited, and there was a lot more of various nasty stuff that they went through without problem (although it should be noted that for some reason one of Inquisitors that arrived later wanted to use chemical weaponry on Nurgle forces, which was met with reaction along the lines of "haha it tickles").
*Weird thing about Vraks, it's this super important location, holds a vast amount of weapons, distributes them and serves as a collection point other planets send psykers to so they can be held until a Black Ship arrives, and yet Space Marines generally only got involved when the DK had hit a major blockade, like fortified gates they couldn't take after weeks/months or when a chaos marine warband was actually doing stuff. Similarly despite this planet being so important the Sector Command officers kept considering writing it off and pulling out the forces because they were taking years to make any progress. Hell, it took 17 years to capture one city.
Space Marines only got involved when:
1) Alpha Legion was around and Dark Angels apparently had some heretical business to do, so they did, and then did nothing of significance. Sure, they destroyed the star port to deny Vraks reinforcements, but... that happened before the reinforcements actually arrived, and when they did they didn't use any star-port, they just dropped straight to the ground because drop pods are a thing, who could have guessed.
2) Red Scorpions popped up because well, I dunno, maybe their book told them to.
3) Grey Knights and Red Hunters popped up because the war was ending, so they wanted to capture the people responsible after the majority of the work was done by the Krieg, and of course steal the glory. They did have to fight a Bloodthrister, but hey, they only popped up at the very end.
The gate was bombed by bombers (duh) from Imperial Navy. The planet was important, but they didn't consider writing it off, but rather decided to focus more on it to wrap the thing up, and it's not like the reason they were there (unbelievably huge stocks of weapons and ammunition) weren't getting depleted by the war. It took them so long to capture "one city", because the "one city" was in Wh40k scale. It was huge, was heavily fortified, and had stocks of equipment enough for half the Imperial Guard. It also took so long because nobody actually expected Chaos to bring that many forces into the fray, the commander who was winning the war up to that point and got his ass kicked was recalled, but even then he wasn't punished for it because nobody actually expected this form of resistance.