This has happened to me a few times and is really strange.
I wouldn’t call it shared dreaming because I’m in the first person, experiencing the dream and the other person isn’t there.
I’ll have a strange dream - for example being attacked by a mechanical spider or zombies. This isn’t really my normal kind of dream.
I can’t track down where the dream came from and will mention it to someone in my family.
Turns out that someone in the family was playing a video game all day that has mechanical spiders in it. Another day it was the zombies. Another time it wasn’t a nightmare but I dreamt I was a penguin flying around clouds only to find out that one of them was playing a penguin game all day.
This is really strange because it’s like I’m “taking” these dreams from someone or experiencing the dreams instead of the person that they “belong” to.
The last two times it happened they were nightmares (which I don’t have many of) and I woke up with a very painful headache.
Anyone here have experience with this? I don’t even know what to call it.
I’ve experienced something like this.
My dreaming group recently decided to try incubating dreams for each other. One of us says, “I’m having this problem, X, could you please dream a solution for me?” and the rest of us do incubations and spend a few days watching our dreams for any solution.
Three of us now have reported having dreams that “don’t seem like our own dreams.” For instance, on an experiment night, I had a (non-lucid) dream in which I wasn’t myself, but a muscled barbarian adventurer. The dream didn’t seem to relate to my life at all (it featured no one I knew, and none of the symbols were meaningful to me), and I can’t ever remember having a dream like it. But it was exactly the type of dream that my friend JB would have—and he was the person I was dreaming for. When I told him the dream, he saw meaning in it.
I had a second dream, on an experiment night, with situations which were important to me at one time, but not in present time. I was surprised that I had the dream because the issues hadn’t been on my mind, and the message of the dream had already been applied in my life. But JB found it meaningful, because he’s facing issues that I had been facing a couple years ago.
The others have reported similar feelings from the experiment.
mhmm…
maybe you saw/heard that person play the game before going to bed, but didn’t really pay attention to it and forgot, but your subconscious took it out for the dream?
maybe it’s also just coincidence, we dream of lots of stuff in just one night, and often it’s enough to think about something related (like the penguins) and you will suddently remember a dream you forgot
dreamosis - that does sound similar, especially the feeling that it’s not “your” dream. Interesting that you were trying to connect with those people - in my case I’m naturally connected to and worried about the people who’s dreams I seem to be having since they’re in my family. I actually have been wondering if I’m trying to protect them by “taking” these dreams and dealing with them so they don’t have to, e.g. as a way of protecting them.
noobdreamer What’s weird though is that in the spider dream - it just wasn’t like a dream I would have. And this spider would bite me and latch on but I’m not really afraid of spiders and I would pull it off and be like what the heck. It’s like it was a kids nightmare and was almost amusing, if not disconcerting. It just didn’t “fit”. Anyway I was hoping there was a name for this 
Have you heard of the experiment with the monkeys on the island? The would be given food that was dirty. Now the monkeys loved the food, but hated the dirt. Well one or two monkeys realized you could wash the food in the water to clean it. The nearby monkeys didn’t catch on quickly, but slowly. Eventually though, when enough realized this trick, monkeys all over the island began to wash their food in the exact same manner.
The above speaks of something like a "meta-"consciousness, a global consciousness, one that stretches between the masses. Humans have also demonstrated this phenomena with an experiment involved in recognizing faces inside an image.
Now, it’s a little difficult to see how this might apply to your dreaming phenomena, but think about it this way: during sleep your mind is most open to suggestion and manipulation. For example, I once was sleeping and my brother’s alarm clock went off and I heard the beeps in the dream.
Yes it could have been you just heard the spider / zombie / penguin game and it leaked in via Daytime residue, but perhaps, dreamosis you in particular, you were more able to pick up on the whims of another mind because you were asleep and something of their thoughts leaked into yours.
Obviously this is all metaphysical in a sense, and it’s only theory, but I thought it sounded interesting enough to mention it. 
i had a wierd dream of being some one else then i saw my self trough the someone elses eyes. heres a little of this ND. i was a captured french person trying to escape from a military base there were other french captives but i was the only one that escaped i dont know exactly what race the military base was but they did speak english. there was a hand full of rebals helping me i saw myself in the mix as well. the rebals and my other self led the other me that was french and in first person to a basement stairwell with a secerite passage to a river. i then went up stream to go back to where me the french person came from. i went through some obsticals and ended up being at a dinner table with a family with me being a french foreign exchange student. then i woke up. i have not seen any french people before or after this dream nor any movies or anything to do with frech. i did have a dream before of being in france though as myself but again was not envolved with anything french and never been to france never even thought about going. i dont know what it could mean if it even means anything. sorry thats the best i could explain it.
My theory is that the way humans “connect” with subtle touches can lead to entering what they see in a dream, not shared really, but just from communication you see clearly what they see from their eyes. Like pheromones! Controls you even though you only subconsciously smell them!