It doesn't look like that amplifier has discrete 5.1 inputs. It's either doing matrix decoding or it has SPDIF inputs (maybe below the stereo game inputs) for AC3 and/or DTS. Of course, this could be a white van special which handles neither of those things.

What's the model number of the amp?

It's a Durabrand home theater system ht3915.

There seems to be no "true" 5.1 audio input, just stereo. It might use for example Dolby Pro Logic decoding, but that is encoded in stereo signal.

Yeah, at best it's doing matrix decoding, but Lennoxx aka Durabrand doesn't appear to license anything from Dolby (or anyone else). Cheap and nasty. Don't expect much.

Cheap yes, but not nasty actually and produces a decent sound which is a darned sight better than the TV does.
I dug out a nice Audigy SE which works beautifully with Windows 10 so let's see what it can do.

I guess I'm being persnickety, but "better than the TV" is a pretty low bar. The nasty is likely waiting for you under the skin. If you open it up, I expect you'll find an undersized transformer and a few single chip amplifier solutions mounted to completely insufficient heat sinking. Everything built to a price.