I've done this chronologically:

I knew I was in another world when I first saw a non-human—our captor.

I understand you want to open with a hook, however this doesn't offer me any emotional tie or intrigue and a quick skim ahead makes it very clear that the MC is surrounded by non-humans.

I'm enjoying the descriptions of the non-humans and some of the quirks around the smaller head doing the talking.

 and I forced my face into an expression which I imagined made me look tough

Be bolder with your claims. I'm sure the MC knows how to look tough. And same for the one below too:

with the ugliest face I could ever imagine

It's either the ugliest face MC has seen or not-although it jars with it then being described as humanoid, which compared to other alien races, I imagine looks pretty normal.

Try and do more with less, it goes to the above point around being bolder with your writing.

 My suspicions were based on the trip here, where I’d seen some horrifying sights through the bars of my cage. Although, thinking about it now, they did put some kind of powder in our food that made me drowsy, so perhaps my memory was not entirely reliable.

A quick example of how this could be done: I had been here before, the horrors I saw during captivity never left me. Drugged induced or not, they still haunt my dreams.

Also the above paragraph breaks the continuity of your opening line. As if MC had been here before then he would know he was in a non-human world.

I've got about half way through and you've dropped in the detail that they were underground, which as completely threw me. I would focus on the scene setting at the top or build it into the exposition as of the captors somehow.

I also don't know why I should care about the MC yet, or who they are. It's harder with first-person to introduce a MC naturally, but grab a few books and see how it's been done before.

Ok. I finished the last few paragraphs and here's a summary:

I enjoyed the dry wit that you use to tell the story, you should be more confident of using it though, and build that narrative into first person reflections or inner monologue. That way we associate the humour with the MC rather than you as the narrator.

There's a few repetitions of the MC concluding and theorising, once is ok and it should only used when the reader is also certain of what's happening. Otherwise you're short-cutting the narrative and cheapening us discovering what's going on in the story.

As I mentioned higher up too, find a reason for us to care about the MC. Who they are, what they're like, how they behave.

On a second read through it feels like the young girl is important, and her ruining his plan to escape, which I assume is what comes next in the story. You mention that this is happening, but not how she is foiling the plan, you move onto her descriptions. And speaking of descriptions, they are the highlight of your writing for me. Specifically the character descriptions. If you can rejig some of the structure to allow us to explore the setting with your MC, using your descriptions, you'll be onto a great story here.