The formal conceit of Fail-Safe is very clever, and in my opinion underutilized (not (Spoiler - click to show)the twist, I mean, just the PC-narrator split). Other than Deadline Enchanter, which was doing a bunch of other weird formal stuff as well, I can't think of a modern game that has really tried this in a longer form. I think "giving commands over a staticky radio" was a great formal conceit in terms of reducing the artificiality of the interaction, and made what would otherwise have been some pretty hum-drum sections much more engaging.
From a modern perspective, some of the puzzles in this game are probably slightly "unfair" (for example, at one point you have to remove an obstacle to moving in one direction, but even after you've successfully removed it, the text doesn't make clear that you can actually proceed). Normally, I can't stand stuff like this, and it makes it hard for me to complete a game, but Fail-Safe is so short and straightforward (puzzle-wise) that it wasn't a big impediment, even for me. This is a classic that absolutely holds up.