Having a frank and vulnerable discussion of your trauma with someone you have emotional intimacy and trust with is incredibly important and can help the healing process. I'd highly encourage people to do that.
However, I think the term "trauma dumping" often refers to the practice of sharing your trauma with people who you don't have a close relationship with, or with people who you haven't interacted with long enough to generate trust.
I am a former trauma dumper, and I dumped my trauma all over a person who I should not have. That person turned out to be a very untrustworthy person. Their knowledge of my wounds allowed them to do some incredibly harmful things to me over the course of an eleven months relationship. I managed to escape, but it was a bad move, and I learned to become more careful about who I shared that information with.
Plus, there is always more to you than your trauma. It certainly doesn't feel that way when you're really stuck in it. Hell, me saying that may have just made some people very, very angry. I got really angry when my therapist said that to me, because it felt like she was minimizing what I went through.
I came to understand that she meant I was an adult with passions and a whole life, and that adult is what I should share with people. By letting my adult self live in the present, I became more able to take care of my trauma using the inner child metaphor. My wounded inner child is precious and deserves care, and I share that with people who will appreciate that. The adult that I am also deserves to live and see the world, and deserves to be recognized by friends and family. Trauma dumping inverts that.
People stop getting to see the awesome person you grew into because humans are wired to pay attention to wounded children, be they physical or metaphorical. Some people will be tender, some will be dismissive, and a few people will take advantage.
So yeah, please share your trauma when it makes sense to, with people you love and trust. If there's a mutual understanding, then any sadness they feel will likely be offset by the warm knowledge that they've helped you make it through another day and maybe heal a bit more. That's what is shown in this meme. Let your adult self live your life the rest of the time, and use that adult to give the kid the care they needed but didn't get.
(Wow, now that I'm rereading this post, I feel a strong sense of irony. Like, it's not a trauma dump, but also nobody asked for me to write a fucking essay about a meme lol)