Nice to know people out there are thinking of us, haha.
I'm at least passingly familiar with both canons (though it's been years since I read Homestuck and I never actually played TF2), and I dunno, this doesn't seem that bad to me. I think both universes have a loose enough relationship with science that you could technobabble up an excuse for them to meet. I'd even accept "a wizard did it" from Homestuck. It doesn't look like the author has bothered thus far, but still, I don't think the crossover is inherently that much of a stretch.
The writing itself is mediocre and I can't detect much comedy in it, but it's not godawful. Some tips on how to properly punctuate dialogue could make a big difference. Some less obnoxious Troll quirks would help, too.
As for the "plot," I think the author just wanted their OC and Sniper to meet and came up with a loose premise to make it happen? At least they're just having a conversation as of chapter 2; it's silly, but not wildly antithetical to Sniper's character as far as I can remember. Not interesting to me or 99.9% of anyone else, probably, but just being boring has never been a justification for a PPC mission.
By the way, we have a wiki with several FAQs and other help articles; it would have answered your question about PPCing original works (in a word: no). Give it a look!
~Neshomeh