To determine whether a desire for X is intrinsic, suppose that you could be guaranteed all of the consequences of X, whether or not you actually get X itself. Would you still want X? If so, the desire is intrinsic, not merely instrumental. (For example, I have an instrinsic desire for happiness, but a merely instrumental desire for wealth.)
Perhaps Reiss' point is that almost all of our everyday activities involve at least some degree of extrinsic motivation. So the distinction might not be especially useful, but that of course is a very different claim from the article's title: "Intrinsic Motivation Doesn't Exist". (It's also worth noting that Reiss mentions "16 basic desires" which sound a lot like intrinsic motivators to me.)
The article also discusses an alternative conception of instrinsic motivation:
One common definition, for example, is that intrinsic motivation is that which is inherently pleasurable, while extrinsic motivation is not. For example, the argument is that children are naturally curious and enjoy learning for the joy it brings them. Grades, they argue, are an extrinsic reward that fosters competition and makes learning less pleasurable.
Note that this is a very different concept. A hedonist might have an extrinsic desire to engage in intrinsically enjoyable activities, as a means to satisfying his intrinsic desire for happiness. But even this definition points to something very real: there's no denying that we find some activities pleasurable, and others onerous. When we have other, external, reasons to engage in an onerous activity, let us call this "indirect motivation", whereas "direct motivation" is for an intrinsically enjoyable activity.
The practical side of the debate seems mostly concerned with the practice of offering external rewards for (purportedly) intrinsically enjoyable activities such as learning or sports. Reiss opposes those who would say that it's better to do such activities for their own sake. He also denies the relevance of research showing that people are less likely to engage in previously-enjoyed activities after being offered rewards for them.
Reiss said proponents of intrinsic motivation are also making value judgments by saying some types of motivation are better than others.
"For example, some people have said that wealth and materialism lead to inferior quality happiness, but there is no real proof of that," he said. "Individuals differ enormously in what makes them happy – for some competition, winning and wealth are the greatest sources of happiness, but for others, feeling competent or socializing may be more satisfying. The point is that you can't say some motivations, like money, are inherently inferior."
Well, I think we can sensibly talk about 'higher' pleasures, and there's certainly nothing wrong with making value judgments(!) But there are good pragmatic reasons for encouraging instrinsic appreciation of worthwhile activities, since that way people will continue to be motivated even when external rewards are not available. Further, it seems that direct motivation is often more powerful - for example, there's little question that those students who are genuinely enthusiastic about a subject tend to succeed better at it than those who are merely motivated to get good grades. But I guess this is the idea that Reiss is really attacking - the notion that direct motivation is preferable to more indirect varieties. Hmm. What do you think?