Haven't they had an app for like 10 years now
Does chess.com have a chess playing app

Yes there is an app. And it actually does cover about everything you can do on the website. It does have a small bug with push notifications but it's easy enough to live with.

Thank you. Can you post the download hyperlink?
Please tell me you're not serious...

Thank you. Can you post the download hyperlink?
oh my god, just go to play store/ app store

You can download the app on your phone/device and it will also make sure it is compatable with your gadget. Good luck with mobile chess.

If you are playing a game using the website, you can maximize the screen size by using the focus mode. It takes away almost everything except for the board and clock and the buttons for resignation and drawing.
https://support.chess.com/article/859-what-is-focus-mode-how-do-i-turn-it-on

I do not own a cell phone. I work with a laptop. Is there a download link?
At the risk of wasting keystrokes and assuming you're genuinely unaware, "mobile apps" are for "mobile devices". A laptop isn't considered "mobile". It already uses the website through a browser, so that's what you get. It's superior to the mobile app. If you want an app, then that goes on a phone or tablet. Ie, Apple Ios or Android device.
If you have a minimized board, that's got a sizing icon in the lower right and you can make it bigger. F11 will make your browser full screen (and F11 returns from that). That does away with the taskbar, the browser menus and address bar. The only thing remaining is the scrollbar (if needed).
Focus mode above also will help, but that in conjunction with F11 (fullscreen) will make things as big as possible with nothing else on the screen.

Thank you all. I should not have used the word app. I guess the word I should have used was does chess.com utilize software?

That's pretty universal on all browsers (at least windoze based ones) and has nothing to do with chess.com. Even on a mobile device it'll work but it requires a bluetooth or usb keyboard to be attached in order to actually have an F11 key to hit.

Thank you all. I should not have used the word app. I guess the word I should have used was does chess.com utilize software?
Factually, no. It's a website served up by a server and interpreted by a client-side browser. Purists might say yes because there's code behind much of the site, and some of that does run on your local system. But for the context of your question, the answer is no.
Does chess.com have a chess-playing app? Working with a small screen would be nice to play without a web address bar.