Shouldn't that be "Last Federation, The - Lost Technologies, The"? ;-)

My preferred approach is to have a hidden "sorting name" and a visible "display name", with the latter having the "The" in front where it belongs.

In my opinion? Yes.

Edit: also, can't someone make a learning-English game called "The 'the'" and sell it through GOG? I just want to see them call it "'The', The".

Actually there are tons of games, whose names start with numerals and even periods.
Proof:
https://www.gamefaqs.com/pc/alpha/27-0

Also it has "11th Hour, The" and it has some games starting from "The" though I never heard about those: https://www.gamefaqs.com/pc/alpha/20-t?page=6).

The band might hold a trademark for that name.

I agree. That is by far the best approach.

Multiple things can have the same name, I wouldn't expect your first thought to be of this if someone mentions a videogame called Portal.

The 'The' would not be in the same business as The The as the latter is a music act and the former would be an interactive learning tool, so confusion between the two is unlikely.

I forgot the ":P". :P

This whole discussion started off as a joke, so a tongue-out smiley should not be necessary. :-P
EDIT: Also, don't forget the nose!

I third that.

I remember iTunes having a settable sort field like that for title, artist, album, and so forth in the Info dialog about an item. The information can be kept unedited (thereby accurate) and viewed as it is meant to be without having to visually decrypt it, and the sort field can be anything or nothing.

There was a band named "The The" long ago. Using the approach of twisting the article around would have made it "The, The". Insist on doing that anyway or make an exception?

What if there was a game named "An A"? Perhaps themed around getting grades in school or some such? If ever there was then you'd get "A, An" if rearranging it. Do nothing special, then no exceptions need be made. Everything stays accurate.

"Tongue-out smiley"? No, that should be read as "colon P". As in, "May you pee out of your colon." It's a very grave insult.
...Or is it? :P

Problem with articles and ordering is always amusing, the.

Fortunately all the nice languages (Finnish, Japanese, etc.) don't even have those.

Of course in the true gaming spirit the listing should be "7th Guest, teh", "11th hour, teh" and so on.

For some reason I have the urge to listen to The The.

An "A" would be a game for learning the alphabet and simple words, and the next stage would be The "The" for learning grammar.

It doesn't seem to me that languages have grammar. I think grammar is simply a bunch of observations of language as used by others, especially when taken out of context by the observers.

I would expect a game named The The would be about reordering titles, perhaps with each level having a different set of rules to apply to long lists of ordinary titles, titles with colons and commas, and other variations. Kind of like the way there are several guidelines for formatting bibliographical information. Perhaps each level would display a basic set of rules at the beginning, and maybe randomize the rules for each play through.