The point specific to that example is that もの is written in hiragana, thus, 物 is also possible other than 者, and I think it's actually 物, or connoting both 物 and 者.
As for 愛する者/人 in general, I believe it's almost always used as "the one(s) I love/the subject loves", i.e., 者/人 is the object of 愛する except when used with an object (e.g. 春を愛する人). For the case "the one who loves me", other expressions such like 愛してくれる人 are used to make clear the direction of emotion.