As you see, the article also mentions 美人系 and 可愛い系.
In casual speech, the Japanese sometimes divide the attractiveness of girls/women into categories like
美人系 The beautiful type
可愛い系 The cute type
セクシー系 The sexy type
'愛され系' is not typically heard (and this is probably why the article is using 「」 around it), but it seems that this girl created this category to categorize her own attractiveness as well, namely as 'someone that is easy to approach, that people feel comfortable talking to'.
So 系 here definitely means 'type'.
