...what does this mean: "Additional Notes: Requires Windows Media Player, Internet Explorer"?

Are IE and WMP used to display embedded media or something?

This kind of sounds silly, stupid, absurd, and scary. Also, compatibility issues? I like playing on wine, and these requirements sound fairly painful. The game's apparently received some praise, but it's still quite pricey even with 67% off, so I'm trying to weigh the risks here.

Yes. Here's an official explanation: https://www.gog.com/forum/general/release_distant_worlds_universe_29805/post29 The risk is that Gog won't be able to grant you a refund or tech assistence, since Linux is not officially supported. Reading around, it seems it's not easy to run on Wine, and the promotion is running out so I doubt you have enough time to make an informed decision.
Best thing you can do is do some more research in time for the next major sale.

Alternatively, if you're fine with using Steam, I believe they offer refunds no-question-asked within 14 days of purchase for games played no longer than 2 hrs. You could just try it there, refund it (it might take a while though, not sure how much) and buy it again here if you want a Gog copy.

Mkay. Thanks for the reply. No, I'm not a huge fan of Steam, and especially not running Steam inside Wine. It's been fairly annoying in the past too.

But well, I just remembered that I have a VM with Windows XP installation for the sole purpose of playing NHL 2004 (which had similar embedded IE6 functionality), so I guess DW:U could work with that too. Oh well, still a little bit of time to consider.