The article overstates the problem.
"Try this scary test to see quite how much detail you lose in your peripheral vision..."
It's not scary, because you don't need to see detail in your peripheral vision. You don't need to read license plates in your peripheral vision, you just need to notice a moving object so that you can react to it.
"However, it is entirely possible for our eyes to “jump over” an oncoming bicycle or motorbike."
That saccadic masking stuff is true, but what the article leaves out is that your peripheral vision is exquisitely sensitive to movement. So, for the split second that you are not making a saccade, if a cyclist is moving in your peripheral field, you have a good chance of noticing him/her.
"We are the result of hundreds of thousands of years of evolution. Our eyes, and the way that our brain processes the images that they receive, are very well suited to creeping up on unsuspecting antelopes and spotting threats such as sabre-toothed tigers.
These threats are largely gone and they’ve been replaced by vehicles traveling towards us at high speeds. This, we’ve not yet adapted to deal with. "
A minor point, but the first sentence is way off. It should read 15 million to 3.5 billion years depending on what you mean by "we are the result of."
But the main point of the article is wrong, because there isn't much difference between a charging tiger coming from your side and a cyclist coming along the road from your side. Our visual system is well-suited to detecting both of those things.