That recipe, which I've made many, many times, yields approx 5-6 dozen cookies if a rounded tablespoon is used as a gauge. For that amount of dough to only yields 2 dozen cookies, they would each be approx. the size of a golfball, maybe. I believe your recipe has a mistake in yield. Check out this link to a similar recipe (nestle Toll House cookies):
http://www.verybestbaking.com/mobile/detail.aspx?id=18476
Assuming you bought a rice cooker designed by a Japanese company (and apparently even other brands tend to meet that market's expectations), the measurement is 1-gou, slightly more than 180ml, which, by no coincidence, is also the typical measure of a wooden sake, cup, and is closely associated with a historical sake bottle size (approximately 1.8l)
http://en.wikipedia.org/wiki/Masu_(Japanese)
It turns out that this amount, 1 gou of dried rice, neatly corresponded to a typical serving of rice. In practice, most contemporary Japanese eat about 1.5-2 gou per day; 1 gou of dried rice cooks up enough for 2 Japanese adults for one meal if you have several side dishes. There are other measurements that derive from the gou (or perhaps the other way around), such as the koku, which was considered the amount of rice that a single person would consume over the course of a year.
This is one of the human-centric forms of measurement that has survived the metric push; you can find various examples of this in many otherwise metric-converted countries. It turns out some studies show that those metrics often make certain categories of estimation easier for people.
Edited to cover the concern about matching the right amount of water:
It's worth noting that you don't need perfect precision for the amount of water, as long as you cook with the full cycle and not one of the express cooking modes. I can't remember the exact scientific principle behind it, but perhaps something to do with osmotic pressure. Some people use the remarkably effective method of measuring a certain amount of space between the dried rice and the water based on the size of their forefinger segment or thumbnail. It apparently works well for almost any imaginable size of pan (though you can have other problems with a pan too wide to have the rice cover the bottom). (Some types of rice do prefer more water than others, but within a single type, you have a fairly flexible range for the water ratio)
Best Answer
Well, after this came up in another question and after realizing data on this was hard to find online, I pulled out my graduated cylinder and tried it myself.
As noted in comments, measuring sugar by volume is very inexact. I found that simply by pouring sugar into the graduated cylinder and tapping it, I could start with about 110mL and tap it down to about 90mL. Even without considering other problems like possible clumps in sugar or the fact that different brands of granulated sugar may have different particle size (and thus different densities), this is already a huge source of potential variation.
So, I tried getting a volume of sugar that was about 100mL on average (that is, tapped down to settle slightly, but not completely). Using 100mL of water and adding this volume of sugar gave me a solution of approximately 158mL.
That means the combined volume of the dissolved sugar-water mixture was about 79% of the combined volume of the original sugar plus water. Again, I note about a +/-10% variance in sugar density depending on how it is measured, which means the possible range here should be around 76% to 82%, depending on how "settled" the sugar was when I measured it. This is in close agreement with widebandit's post here that found a ratio of 25 fluid oz. solution to 32 fl. oz. of original ingredients, or about 78%, though just a bit higher than Jeff Axelrod's ratio of 75%.
Maybe someday I'll try this with a few different brands of sugar, but I just thought I'd add one more datapoint that's close to the other answers here, with some information on how much variance to expect.