Is video proof absolutely necessary for a run to be accepted? I want to start running this game but don't currently have the money to purchase a capture card.

No you're all good with no video, but i would ask for u to link a picture (preferably twitter if you have one) with the Splits/Time. Also if you want to look into a cheap cap card, easycap are usually under 15 dollars and a good starting place. I don't imagine this game is gonna have 20+ runners, but if it does get there, thats when video proof will become a thing.

I feel a link to a screenshot of the time, a picture of the scorecard and pic of character (for World Tours)