If someone would have asked me that a year or so ago, I would have had at least some rough idea of what aikido makes Aikido (tm) to me.
But, now, I'm beginning to understand that it is a very hard thing to define Ueshiba Morihei's Aikido. Let me try to put my thoughts down on why.
1. The basics. Ueshiba Morihei had them. Got them from Takeda. Gave them to Tomiki, Shioda, etc. In fact, I think quite a few of his students got the very basics. I'm not talking about rote jujutsu, but more along the lines of aikijujutsu (Taking a guess, I'd compare this to pulling silk and some of the Aunkai basics.) However, not all the direct students taught this feature. Tohei tried to keep it intact in his school. I think that some higher levels in all aikido schools eventually get a good bit of this. But, this doesn't really define Aikido as a lot of other martial arts convey the same basics, including Daito ryu.
2. The Internal skill. Here is where things get more strict. This is the area where Ueshiba could not be pushed over, where his students said he felt like a ghost, where Dobson felt like he hit a wall when he body slammed the ukes trying to push Ueshiba over, etc. This would be aiki no jujutsu (I'd compare it to reeling silk). Not many of Ueshiba's students learned this. I'd venture Tomiki and Shioda had some measure of it. I really don't know about Tohei. However, as #1, this really doesn't define Aikido because you can find these skills in other martial arts, such as Ushiro's karate, Okamoto's Daito ryu, and some Chinese masters.
Now, before I move on to the next part, I'll make a disclaimer here. While #1 and #2 really don't "define" Aikido, per se, they *must* be present or you have no Aikido. In other words, you can have #1 and #2, but still be doing another martial art. If you don't have #1 and #2 in some measure, you aren't doing Aikido.
#3. Spirituality. There is a place one gets to when one has trained long enough that one understands that there are choices available for a martial outcome. Instead of mere self defense and living, there are options open that include breaking, damaging, killing, etc. But unless one has the skill level necessary, these options are theory only. I certainly am not at that point, so I go by theory alone. Ueshiba had that level and he chose options that were more attuned to discarding an opponent (NOTE: this doesn't mean peace and harmony and loving an attacker) rather than break/kill at his feet as the old jujutsu would have done. Being at this place doesn't necessarily define Aikido, because you can find this theory in a lot of spiritual areas. However, most lack #1 and #2 above, so they can't back up their theory and must use other means available (like peace talks.)
#4. Way out there. Yeah. Kami, neo-shinto, bridges between heaven and earth, channeling kami, divineness, etc. And let me be clear. You can not "find and replace" the word "kami" with the Christian "God". It doesn't work that way. Conversely, yes, the Christian God can be a kami. But, still, Ueshiba was really out there compared to most people. He did believe that you didn't necessarily have to trace his footsteps, but you could use other ways to get there. I believe that, too. But, I think you're still going to have to get to the edge to try to understand what he was doing, what he lived, and how all this intertwined with his martial ways. He didn't just live martially and belong to Omoto kyo. His whole life was a fully integrated mesh of them both, in a manner beyond other martial spiritual practices (such as studying Zen meditation while also studying karate.) As the first three, you can find people like this in other areas.
But, if you are working on having all four. Not 3 out of 4, not 2 out of 4, not 1 out of 4; but all 4, then, I think you are studying Aikido. And working to gain them is the path for what I believe makes aikido Aikido.
Working on #1 & #3 might be construed as Ueshiba Kisshomaru's aikido, but it isn't Ueshiba Morihei's Aikido. Doesn't mean it's wrong or bad, just that I don't believe it's the founder's Aikido. Depending on the school, working on #1 through #3 can be considered aikido, but it isn't the founder's Aikido. You might get close enough that the lines blur. I dunno. Everything is a theory and a work in progress.