My assumption is, that it's not chrome that's opening the links, rather a different app that you might have installed at some point. (That's because chrome never opens links in the way you have it in the screenshot.) This app it' now the default for opening links.
You'll have to clear it's defaults in order to make chrome the default again. If you know the name of this app, go to settings/apps/[name of the app]/defaults/clear defaults. Next time you open a link, it will ask what app you want to open it in, select chrome or other normal browsers as default.
If you don't know which app it might be, then clear defaults for all apps. Go to settings/apps press on the three dots menu and press on reset app preference. This will not delete anything, but it will change some settings to the default
