Well, almost a year-and-half later Google has completed the job and now, Chrome browser will not be able to access or install any apps from the store. Google announced this via a blog post on 19th August 2016 and now have updated the blog post on 5th December 2017, making the change live from today. Chrome will not fully remove support for Chrome Apps on Windows, Mac or Linux until after Desktop PWA installability becomes available in 2018. PWAs can work across multiple browsers even on mobile devices, and can deliver an app-like experience to desktop websites. Google sees PWAs as the future, thanks to their superior offline capabilities, efficiency, and uniformity across platforms, but they're functionally similar to Chrome Apps, which are somewhat unintuitive by comparison.
Google, in a blog post from August previous year, said that the apps project had failed, with just about 1 percent of the total users from Windows, Mac, and Linux actually installing and using them on the Chrome browser. The Web Store will only have Extensions and Themes available for download starting Wednesday.
If it sounds complicated, you can check out the Google Support documentation which takes you through setting up and using Chrome Remote Desktop on your Windows, Mac or Linux PC or Chromebook. This extension enables you to install, view, and modify the Chrome Remote Desktop native client from the web UI. With the shutdown of Chrome Apps, Google is working to bring Progressive Web Apps (PWAs) to the desktop.
Google had big plans for its progressive Web Apps. There's still no word on removing Chrome Apps from Chrome OS, though.
According to Ars Technica, Google is directing developers towards a different way for desktop: Progressive Web Apps (PWA). "We have been investigating ways to simplify the transition for developers that depend on exclusive Chrome App APIs, and will continue to focus on this - in particular the Sockets, HID and Serial APIs".