On some websites, why doesn't Ctrl + Click work, but right-click > Open in new tab, does?
Solution 1:
It is because of JavaScript that captures your clicks and, because of that, interferes with your keyboard shortcuts. If you disable JavaScript then shortcuts should start to work again. You can test it by pressing CTRL+SHIFT+I (Developer tools), then clicking Settings (gear icon) and enabling option Disable JavaScript.
Solution 2:
Middle-clicking seems to work like a ctrl-click (as mentioned by Firelord in the comments).