Plugin that is no longer supported on WP

So I work with a plugin for petfinder, a plugin that helps non profits like dog rescues and animal shelters post their homeless pets for adoption. It simply queries petfinder to pull down the animals you uploaded so you can keep your site updated with the pets you are trying to save. Well it was a useful plugin, but it has not been updated for two years. I am not much of a coder, but I am thinking of trying to recreate it so it works again (it works on some theses, but it is wonky and does not work all the time). Can I use the base code that is already there to recreate the plugin? Or is that not cool, not legal, etc. ? The plugin is here: