What is a “variant article,” please?
Pretty long time since this was posted. Maybe you already found out what this means or it is not important anymore 
Normally ‘sko’ is classed as a masculine noun in written Norwegian (both in Bokmål and Nynorsk). This means it should have the article ‘en’, not ‘ei’. But for some dialects this word can be classed as feminine or even change class depending on speaker. So my guess is that whoever put this in to the course you’re doing based it on a dialect of spoken Norwegian where ‘sko’ can be a feminine noun.
Maybe adding to the confusion is the fact that when you write Bokmål in Norwegian you can choose to either use the ‘en’ or ‘ei’ article for nouns classed as feminine. So both ‘en kvinne’ og ‘ei kvinne’ is considered correct. The reason for this is that in a lot of Norwgian dialects the words before considered feminine are converging into the masculine class so that they only use two noun classes insted of three. If you come from a dialect where ‘sko’ is feminine it isn’t really something you would think about because you are so used to seeing feminine nouns having both ‘en’ and ‘ei’ in writing that it wouldn’t be strange for you to see ‘en sko’ all the time.
Thanks. Although I am also doing a written course in Bokmal Norwegian.