The generally accepted reasons for the relatively low death toll is three-fold.

First, the Hindenburg was relatively close to the ground when it ignited, as it was coming in for landing. Additionally, it fell relatively gently, as you can see from the movie footage of the disaster. Not all of the hydrogen ignited at once, maintaining some buoyancy for critical seconds, lowering the craft a bit more slowly than freefall. This allowed many of the passengers and crew to jump to the ground. Though many of them were injured severely by the fall, they were able to escape the fire. If you look at the diagram of crew locations, you'll see that most of the survivors were located near the bottom of the craft as well as being near windows they could egress from. Most of the crew located in the inner portions of the craft died as they were too high up to survive the fall at the point when ignition occurred or unable to get out quickly enough.

The second reason is that the majority of the fire was caused by burning hydrogen. Hydrogen is extremely low density, especially as it heated up from combustion. As you can see here, the hydrogen is rising relatively harmlessly as it burns. Obviously, this didn't do the crewmembers in the forward parts of the vehicle any additional favors (The vehicle buckled and so the nose of the Hindenburg ended up going into the column of burning hydrogen), but it did avoid most of the passengers or crew who were concentrated along the bottom. Burn injuries were extremely common, but most of this is attributed to burning debris and diesel fuel raining down on everyone.

Third, the disaster occurred at the landing site. There were numerous Navy ground crew in place to secure the Hindenburg who were able to rush in and help survivors clear the area before burning wreckage crushed them as well as providing emergency medical aid at the scene. Also, there was a road, casualties could quickly be evacuated to nearby hospitals. Large sections of New Jersey are filled with dense, marshy forest, which would have greatly complicated access to the crash, had it happened away from the landing zone.

All in all, it's very lucky that this occurred when the Hindenburg was so close to the ground and landing. Other incidents such as the Akron had few survivors. If the Hindenburg had ignited even a few minutes earlier, it's quite likely there would have been few to no survivors.

This is an excellent source: https://www.airships.net/hindenburg/disaster/ It has copies of both the US department of Commerce as well as the German disaster reports.

The footage is somewhat deceptive due to exposure and our unfamiliarity with airship operations, and the whole story is known as a famous disaster in no small part because it was a famous flight caught on film in an era when smartphones and video cameras were not ubiquitous. It's possible that this was the first example of a live disaster recording played on-air for a national radio audience in the United States, and in any event it was easily the most well known example in at time when this wasn't common. Both of these factors set an expectation of the disaster death toll that isn't entirely in-line with reality.

Today, coverage of such a cataclysmic event would almost instantly be broadcast out over the airwaves. But, in 1937, satellite relay and other such options did not exist. Furthermore, at that time, NBC maintained a policy against the airing of recordings on their network. It was a policy they relaxed the day after the Hindenburg tragedy in order to air some of Morrison’s remarkable, eye-witness account.

The effect of the Hindenburg recordings on audiences was startling. Never before had such a large audience heard such a blow-by-blow description of such a horrific occurrence. For listeners, the news of the day suddenly became active, proximate, real.

News gathering and reporting was altered too. Though reporters had been witnessing devastating events for decades, previously, they had the benefit of time and distance—both emotional and geographical--between the things they observed and what they eventually wrote for publication or broadcast.

This Pathe film shows quite a bit more context than the usual short clip, particularly as the Hindenburg circles to release ballast. You get a much better sense, with the proper exposure and framing, of the altitudes scales involved.

It's important to remember that the Hindenburg was at low altitude (no more than 90 metres altitude at any stage) and in the process of mooring when it caught fire and, in spite of the fact that the fire consumed much of the hydrogen, it didn't ignite instantaneously. Thus the Hindenburg settled onto the ground rather than dropping without any lift at all (the official German report estimates 30 seconds from the initial fire to the first contact with the ground). For the most part the passengers and crew suffered horrific burns, even those who survived, but they didn't tend to suffer the kinds of impact injuries that we would normally associate with an air crash.

If you read the German report on the disaster, it goes into further detail as to the locations and actions of the crew and you can see that the entire crew was at mooring stations at the time and this doubtless reduced the death toll as well, simply because everybody was awake alert during a potentially dangerous evolution.

In essence it was a low speed crash followed by a short but intense fire fuelled by a lighter than air gas that quickly dissipated when the gas bladders were ruptured by the impact and fire as opposed to the sorts of air crashes we're more familiar with today. So combining this with a bit of "luck" and you can start to see how it was a crash that resulted in serious injuries for nearly everybody but killed a smaller number than it would seem.