I have to confess, Joshua, that first reads of both stories left me confused -- though that's not unusual for me with 75 worders.
To take them in turn:
The Aliens
Right, as I understand it, after a thousand years or so a colony ship has arrived at a planet, only to find it already occupied by other humans who, in the intervening period, had developed FTL travel and beaten them to paradise. That it? As a plot, it's intriguing, certainly (though the practical side of me wonders why the FTLers hadn't contracted the ship and given it help in getting to the planet more quickly) but I think it needs a bit of work. I'll red-pen it (well, purple-pen) to show some areas which I think could do with some fine-tuning:
The two [why only two? A whole colony ship and only two survivors seems a bit odd, and if it is only the two of them, it rather reduces the pathos of what follows] stared down at the blue sphere, overwhelmed by their emotions. For 50 [no big deal, but probably better as "fifty"] generations, their ancestors had [definitely needed as the tense is wrong otherwise, but that takes you over the 75 limit] occupied this [confusing -- they're looking at the planet, so "this" seems to refer to that planet] colony ship, fleeing Earth for a new world.
They had [you could make that "They'd" which would save a word] finally arrived.
However, their emotions were shock and horror. [too far from the "overwhelmed" line to be an effective antithesis] This paradise [how do they know it's a paradise?] was occupied [repetition of "occupied" ungainly] by [with] humans who had perfected FTL travel. They [strictly "they" are the FTL-humans, so another moment's confusion before realising who is meant] now had no home and no hope of rejoining their distant cousins. [this floored me. Why no home? They've lived on the colony ship all their lives, so they've a home there for a start. But why can't they go down to the planet? The distant cousins have developed FTL not two heads! (Though it wouldn't be "rejoining" them since they'd never been joined in the first place.) If it's a paradise, the FTLers-- some of them anyway -- must be good people, so would doubtless welcome the newcomers. And they must have seen the colony ship coming for some time with long-range telescopes, so why haven't they contacted these two?]
They had wondered if they would find aliens; they found themselves aliens instead. [A neat line in the right circumstances, but to my mind there's nothing in the story that warrants it]
So, not a bad piece, but not quite there for me, so not one I'd have shortlisted.
The Gods were Angry
This one, to be honest, seemed a bit... um... pointless. Sorry. I get that he's doomed to spend 10,000 years in a desert, but without knowing what he's done to deserve it -- or not -- it's hard to feel anything for him. Why is he cloaked in a dark shroud? What is the shroud, and what does its presence add to the story that you feel it necessary to include it? "Nearly insane" -- surely he'd be wholly round the twist after 1,000 years? And "perpetually on the brink of death" seems otiose. It felt to me that you'd used a lot of words without actually taking the story further, which is fatal in a 75 worder, where every word must count and give value.
I also rather lost patience with him staggering on. Why didn't he apply some sense and just sit down and wait out the years on a dune? Also, the repetition of "staggered" grated for me a bit, which didn't help. As to word use, "sojourn" was for me wholly out of place -- it's a short stay or a visit, and 10,000 years is anything but! I also stumbled over the "lich" and had to check its meaning -- I only know it from "lych gate" with the alternative spelling -- and for a moment I thought you meant "lichen" (which I actually liked, since it gave a barren, scratchy, not-human vibe to the story!). I enjoy using obscure words, but it does render one vulnerable if they're not widely known. And never forget rhythm when you're writing -- that line is bumpy as written, and "more lich than man" is stronger, and gives you two extra words to use elsewhere!
Sorry I can't be more enthusiastic about the two of these, but always remember that all this is just my opinion, and as you'll have seen if you've read earlier posts here, one story can create a good many different opinions! In any event, well done for getting the stories done, and good luck with the present and future Challenges!