Or are people who are at relatively low risk of those diseases more likely to cycle?
Or both?
The way the headline reads, many people will be led to believe "Oh, if I start cycling, then I'll cut my risk of cancer and heart disease."
This study does not lead to that conclusion. All we can say is that there is a correlation between cycle and lower cancer/heart disease risk - even when accounting for a few other factors.
Given that there are other ways of concluding that regular aerobic exercise cuts cancer and heart disease risk - and indeed the preponderance of the evidence suggest that it does.
But I doubt the effect is really to almost halve the risk of those diseases.