Adding fat is part of the meal template, which is a recommendation. You could do a Whole30 without ever making any meal meet the meal template and as long as you followed the rules, you'd still have done a Whole30 -- but you'll get the best results if you also incorporate the recommendations, including making your meals match the meal template.
Here's a little more explanation about rules vs. recommendations: https://whole30.com/2015/01/rules-recommendations/ and the rules are here: https://whole30.com/whole30-program-rules/.
It does count, in that it's a fat, but it rarely ends up being enough. First, many things that you add fat to in cooking, a lot of the fat ends up staying behind in the pan, unless you're making a conscious effort to pour it onto your plate and consume it. Second, if you're cooking multiple servings, you're probably not including multiple servings of oil -- you may add a little extra for 2 servings compared to one serving, but you're probably not completely doubling it, and if you're cooking four servings at once, you're unlikely to be quadrupling your cooking oil, because you really just don't need to. That's why we usually encourage people to include a serving or two of fat, in addition to whatever oil they cook in.
The real test of whether you're consuming a good amount of fat at each meal is whether you can go 4-5 hours between meals pretty well. If you can, you've got it about right. If you're hungry in two hours, something in your meal is not quite right, and fat is something people often underestimate how much they should have. If you're regularly going 6 hours or more before you start to feel hungry, you might need to cut back on something in your meals.