Suppose I tell you about a website, then tell you to go there and become a member, would I say option 1 or 2:
1) Iru tie kaj membriĝu!
2) Iru tien kaj membriĝu!
Since there is no physical movement, is it okay to leave it off?
I would say that it should indeed be number 2 even though the motion is only metaphorical. Imagine if you were to phrase it as something like iru al la ĉefpaĝo. In that case it is clear that the al is necessary which means there is the notion of a direction, even if it is only metaphorical. When there is a direction with the *ie correlatives then it should have the n ending.
For an example of this phrase in the wild we can quote a video from Evildea where he talks about how to install a piece of software and uses iri tien to refer to visiting a different folder:
Do mi nun estas en la dosierujo, kien mi instalis la ludon, sed mi devas iri al la “lingva”-dosierujo en la “data”-dosierujo. Do mi iros tien kaj mi kopios la dosieron.
It's clearly needed. The fact that there is no physical movement involved does not change the gramar. There are many examples for accusative of dicection without physical movment: "Mia koro sekvas la muzikon en ĉiajn ritmojn kaj melodiojn."
the phrase kien mi instalis la ludon seems a little strange to me. I would say kie mi instalis la ludon, for the underlying question seems to be "where will I install the game" : Kie mi instalu la ludon? Nu, mi opinias ke vi instalu la ludon tie en la dosierujo!