Not much composting will happen inside that bucket. It's also far too small -- we'd fill that bucket a couple times a week in the winter, maybe daily in the summer. Your kitchen habits may be different than ours, but my point is that you're going to fill it eventually and then you'll need someplace to put the compost. Also, an outdoor compost pile needs to be around 3'x3'x3' before it becomes very active -- much smaller than that and you just have a pile of rotting garbage.
The container you built does look like a good temporary holding spot for kitchen scraps before you move them to a larger container or an outdoor pile.
If you read the second post in the series that you linked to, you'll see that the author is really talking about vermicomposting (i.e. composting with worms) and uses the small container you built as a temporary holding spot:
We keep our DIY kitchen compost bucket under our kitchen sink until it is full, at which time we feed the worms by emptying the contents into the worm farm.
From what I've read from other sources, worms can eat about half of their body weight in compost per day. So if you have a pound of worms, they'll eat half a pound of kitchen scraps every day.
If you're thinking about trying vermicomposting, do a little more reading -- the articles you linked to are light on details.