If there's one thing Jinteki is good at, it's making the runner make terrible decisions that lose them the game. The classic, of course, is Mushin No Shin--do I run this (risking a Junebug flatline) or do I not (risking a TFP score or a Ronin flatline)? A poor decision, especially late game, could be the deciding factor.
An Offer You Can't Refuse puts this same sort of decision on the runner. If you don't run, the corp gets an agenda point for the low, low cost of 4 and the used to play the card. One point doesn't seem like much--but at the right time, it can mean everything. A Jinteki deck at 3 points isn't so scary; if they Mushin a card, the runner doesn't typically have to check it, because even if it is a 5/3 agenda they can't score out. If the corp is at 4 points, though, that could be the winning agenda, and the runner has to respect that. But the real threat comes at 5 points; suddenly, every unadvanced remote starts to look like a Braintrust or a Philotic Entanglement, and the runner has to start checking them, making it easy to hit them with a non-advanced trap like Psychic Field.
So obviously, the runner doesn't want to let the corp get that point. But the alternative is also pretty bad. The corp gets to choose the server, meaning they will choose the nastiest, the deadliest, or at the very least, the most expensive central server. Maybe they make you run through a Chum in front of a Crick, hitting an Archives with three Shock! and a Shi.Kyū. Maybe they use this as an opportunity to use Batty on Grim, killing your sentry breaker with the Batty'd subroutine so that you lose another breaker. Or, maybe they just make you run HQ, and pull off the Chum+Kitsune+Snare! for six net damage in one hit.
Which option will they choose? Well, that depends on a number of other factors. In the early game, the runner might not have their full icebreaker suite up, and letting the corp go from 2 points to 3 isn't so terrible--most runners will let you have the point to avoid a rig wipe. Later on, though, a fully rigged-up runner doesn't have as much to fear...provided they have the money to run, and if you make the Offer when they're low on funds they might hesitate. Of course, if you can get to 6 points, then the title of the card becomes literal--they cannot refuse without losing the game.
One finer point is the difference between choosing a server with derezzed ice, and a server which they've already run. If the runner can see everything they'll have to deal with, that removes the guesswork. They simply decide which is worse, running the server or ceding the point. On the other hand, if the server is filled with scary facedown cards, they can't be sure what's going to happen--but then the corp has to have the money to not only spend the 4 for the Offer, but also pay the rez cost of all the ice on the server, and still have 4 left over for a Snare!, making this a more difficult kill to pull off. But then again, maybe you can scare them off with just an unrezzed Pup behind a Chum...
You'll notice I've only mentioned in-faction cards. That's for a good reason--at three influence, it's hard to justify including AOYCR in another faction, and most of the best kill-server cards are of Jinteki design. An exception might be made for certain bioroid ICE--because the run is happening on the corp's turn, they have no clicks to spend, making Ichi a scary proposition. However, most bioroids feature "End The Run" subroutines, and if the runner can escape your Offer by bouncing off an Eli you've wasted your time.
So, in conclusion, An Offer You Can't Refuse is a solid addition to the murderous Jinteki arsenal, but doesn't play well out of faction. It goes a long way towards solving the Jinteki problems of not being able to actually score, and not being able to lock down the kill.