Emojis are defined by the Unicode standard, so anyone is free to create images of emojis according to this standard. Apple has created such images, and they are part of the fonts that they are using on iOS and macOS. They are copyrighted, but if you check Apple's terms and conditions, you are free to use their fonts on any device that is legally running iOS or macOS. Likewise, it is very likely that Microsoft, Google and others have created similar images for emojis and have very similar license terms. Your screenshot seems to show an iOS device, so any use of Apple's emojis in that application would be legal. If you copied these images from Windows or Android, they might not be legal.
I recommend that you don't make any copies of the images to avoid problems. On iOS you can display emojis just like you would display any text. You pick a font, you pick a font size, and you draw text just like you would draw the text "abc". If you want these emojis rotated then on iOS you should look at "Coretext" which allows you to manipulate characters on the screen, including emojis, any way you like. Like rotating them, bending, scaling, whatever Coretext does.
If your game runs in a browser, and therefore might run on Windows, Linux, Android or MacOS / iOS, then be aware that the emojis will not be 100% identically, so you should test that they are acceptable quality everywhere. And there are traps: There is a "gun" emoji, and Apple in their infinite wisdom decided it should have a toygun image (more family friendly I assume). So if I added this "toy gun" emoji in my post as a laugh, you might see a real gun emoji and feel threatened. Or someone might send me a real death threat with the gun emoji and I think it's a joke.