Issues with Adobe Illustrator
So I seem to be having an issue with Adobe Illustrator. When I export files I seem to be getting a little pixelation that is bugging me. I'll include the exported images below. But I exported the two images in 72 dpi for screens and when these files were incredibly pixelated I exported them once again in 300 dpi. Exporting them in 300 dpi limited the pixelation but I thought if I'm exporting for screens then the files should be exported as a png in 72 dpi. I'd appreciate any help available.
Just for some context the logo is for a game blog me and my group have made in uni for our game module and the smaller icon is a favicon for the blog.

300 dpi

72 dpi