Once you delve into the article, it becomes clear that it's the changes in the town's infrastructure and urban form that have to be done to enable safe and worry-free cycling that result in a more livable space, where mobility goes up within the town. Cycling isn't the cause; rather, it's an effect of an urban form that treats them as valid form of transport, and doesn't force them to gladiate among heavy cars that go five times faster, or confine them to narrow strips where unprotected pedestrians walk five times slower.
The 'shared space' concept, where traffic-calmed cars are in close proximity to bikes and pedestrians, relies both on traffic devices, the emergent slow speed of traffic to act as a barrier to overtaking, and on the psychological inhibition of drivers to not flaunt the idea and drive like madmen anyway. It also trades physical separation of pedestrians for an emergent one, which is a raw deal for some disabled people (e.g. those with impaired sight, hearing, or mobility), or those with small children. This is a tradeoff that some communities don't find acceptable.
But for the majority of people for whom it works, mingling car traffic, bike traffic, and pedestrian traffic in close proximity has the advantage of decreasing the utility of high speeds that could otherwise be attained by cars and increasing the utility of lower speeds and non-motorized forms of transport. This effect encourages the town's urban form to be compact and provide employment and services close to residences or transit nodes (like train stations), which leads to the cityscape familiar from the Netherlands.
Areas that were developed with the assumption that the sole choice of transportation will be the automobile face many barriers to retrofitting other modes of transport as a realistic choice. This is because density is a key metric: a car covers 20 times the distance in the same amount of time as walking. If there is no employment or services within a walkable radius, any sidewalks or bike lanes are largely for recreation, and don't offer a meaningful everyday alternative to driving. This is why dense areas like CBD Vancouver can mull over these changes, but doing the same in Surrey is a lost cause. In the US, where urban employment is a mix between those living there and those commuting by car from far away, the streets of cities are still dominated by cars that are trying to cover distance in little time. Market Street in San Francisco is chock-full of transit and pedestrians and stoplights, which prevent it from being an urban highway, but other streets in SF are far too rapid to safely host pedestrians or bikes, even though the city around it was clearly built at a time when slower transport was the norm.