<Snipped quote by Yatagarasu>
Basic noodles like these are good.
*looks at them*
The ram was surprisingly like my home’s ramen, and these noodles look and smell like my home’s too.
*looks at you*
I never thought about it until now, but I wonder how similar we are. I half expected the foods to be called something wildly different. But still have something that would note of my home world when inter-dimensional travel was a theory. You and your children are obviously not from my world, yet you all are very similar in basic terms. Do you consider yourself human?
That's a hard question. I'm factually not one, at least as you understand "humans" to be. I look like one, I used to be one, but at present I'm not built like one. For example, if you looked at my blood in a lab, you wouldn't see DNA like you have. The entire genetic system is different, and I considering what world you came from, I highly doubt it could support an environment where life can come about with it.
I'm sure you'll come across people who are even stranger, though. A fun example is that there is a world of equines, who have access to magic and all sorts of other fun resources, but outside their home they mostly take humanoid forms. There are hypotheses about why, but in practice it seems to be the same as... programming languages, perhaps. Sure, you can write in any language you want and get the same result, and each person has preferences, but it's easiest for everyone to share a singular one. "Human" is that common language, in my experience. Or at least the facsimile of it.
Though for your other realization, normally beings that can travel between dimensions have some way to translate speech. They'd be pretty stranded otherwise. But in our case, we happen to already speak the same language, with similar terms for things, because I was from a similar world.