This EMIYA has no recollection of a relationship with Rin as Shirou cuz that is not his timeline. We also do not know what kind of relationship this timeline's Rin has with Shirou. This doujin is more inspired by 2 things:
1) Isthar does show some interest in EMIYA. Whether this has anything to do with Rin's influence is unknown.
2) Rin is always paired up with EMIYA instead of Shirou because she has a much closer relationship with EMIYA, so much that her romantic relationship with Shirou in UBW route can only make sense in light of her relationship with EMIYA (in the original visual novel anyways, the anime tried to remedy this with varying success). This is why she is often considered to have the weakest romance with Shirou and why the status of UBW being her route is sometimes mocked, like in the doujin "Unlimited Saber Works."