If you can stream from a laptop webcam, there's an answer.

If you can't, what I suggest is saving up for a Cap Card (they're not expensive) and in the meantime practicing, so that when you do start running the game on video the runs are actually good!

^ What Laurie said.

Composite cable Capture Cards don't usually go more than roughly 50 dollars for a more than decent one. Some are also in the 10-ish dollar range. You can decide to get a really cheap one like an ezcap which is like 7 dollars. In the meantime save up some money until you can afford a slightly better one.

While the rules do say Video is required, don't let that stop you from doing runs at all. So my recommendation is maybe start submitting runs when you do get a capture card. But practice and do runs in the time that you have before you can get one.

another alternative is emulating until you do have a cap card, since recording with emulator is fairly easy.