Because of the Canis Helix the Space Wolves can only recruit from people that are from Fenris, this is the primary reason the only known Space Wolves successor chapter has gone extinct(before the coming of primaris).
All recruits that are not from Fenris simply reject the gene seed or die in the process.
So how were there Space Wolves before the discovery of Fenris and how did they survive the Canis Helix?
The Space Marines, or Legiones Astartes, were created from the research of the Emperor himself.
During Terra's isolation during the dawn of the 31st Millennium, the Emperor had striven to create twenty superhuman beings. These Primarchs, as he called them, were genetically engineered creatures, artificial humanoids with astounding abilities. Each was created differently and with his own unique skills, powers, and in some cases, incredible psychic potential. The Primarchs were made to resemble Humankind, but many were mighty in appearance. Yet the Primarch experiment never reached its conclusion. In a disastrous incident, the nascent creatures were swept up by terrible forces that dwelt within the Warp and scattered across the stars. Rather than trying to duplicate the long and arduous work through which he had created the Primarchs, the Emperor instead used the raw material developed during the Primarch project to create the Space Marines. After much toil, the Emperor created a number of artificially cultured organs, each re-engineered from the gene-banks of the Primarchs.
These "organs" are the Gene-seeds of the Primarch, and the "Canis Helix" was named due to the fusion of the Emperor's own DNA, with wolf DNA. This is how the original VI Legion was created.
However, you point out that all other recruits reject the gene-seed or die. This is not exactly accurate.
Following their reunification with their Primarch on the frozen Death World of Fenris, the stabilising effects of Leman Russ' own gene-helix pattern over the existing VI Legion's gene-seed seemed to have all but reversed the prior difficulties of candidate survival. This, combined with the Fenrisians themselves who proved to be extraordinarily resilient genetic stock -- attributed to long-term human survival on such an inhospitable world -- ensured the successful transformation from baseline human into a transhuman Astartes.
This is in reference to the creation of the VI Legion using the gene-seed the emperor created; meaning that not all initiates died or rejected the seed, it was just incredibly difficult to find sufficient subjects for the job.
So, when the Emperor and Leman Russ were reunited, this became much easier to create Space Wolves, by stabilising the gene-seed implant with Leman Russ' own DNA, by way of drinking his blood:
When a Space Wolves Aspirant is deemed worthy to join the Chapter, he partakes in a sacred ceremony where he imbibes the Canis Helix, the Spirit of the Wolf. In actuality, this is a genetic cocktail drawn from the genome of Leman Russ and used as a catalyst to activate the genetically-engineered viral machinery of the Aspirant's gene-seed implants
When Leman Russ disappeared, this then threw a spanner back in the works, since Leman Russ' DNA was no longer available to stabilise the gene-seed implanted in new initiates.
In addition to all of this, the Space Wolves are more of a Tribe than an "official" Legion, as they only choose to follow Leman's Teachings, ignoring the Codex Astartes.
This is probably where the confusion that Space Wolves only come from Fenris - not because they are the only ones capable of successfully integrating the gene-seed of the VI Legion, but because they feel only they are worthy of it*.
*This is my own speculation, I do not have any evidence to support this belief
From your own link
The effects of the Canis Helix only became apparent over time as the early generations of the VI Legion's intake aged [...] this instability was greatly ameliorated after the Legion's re-unification with its Primarch Leman Russ
So the original Space Wolves survived because the genetic instability took a while to get going. We might speculate that they also didn't drink the "Cup of Wulfen" at that time, which greatly accelerates the process in post-unification recruits.
Before Russ was discovered, the Wolves were a bunch of dicks. They were uncontrollable bullies. They were developed in isolation along with the Salamanders and Alpha Legion, and were considered a fractious and undisciplined force, to the degree of officers losing control of their troops in the middle of a battle. To make matters worse, they often slaughtered civilians who had no way of fighting back. Their geneseed was also extremely difficult to implant in aspirants, often killing them. https://1d4chan.org/wiki/Space_Wolves
So the answer is that implanting the Spacewolf Geneseed into a human not of Fenris had far more likelihood of failure and when it did succeed it resulted in a marine who lacked the discipline later spacewolves showed. Now it is very lucky for the Spacewolves that Leman Russ landed on a planet full of humans who had been genetically manipulated to be a little bit wolf.
