The language is just really confusing I suppose. At least in normal parlance, "fulfilling the requirements of the law" would imply that some set of conditions had been established that can enable the law to take effect. At least that's what words like "requirement" seem to imply. But clearly that's not what's being talked about here. If I understand you correctly, what was 'fulfilled' was the intent of the laws - the laws were established to make man righteous before god, but an alternative way (Christ's sacrifice) of fulfilling the intent of the laws was used. Which is still kinda confusing for a couple o' reasons:
1) It makes the original laws seem rather pointless then. Which maybe isn't really an issue.
2) Did Christ's sacrifice work?
You are correct in the statement of fulfilling the intent of the law. Your first point of the original law being pointless is correct to a degree. In this forum the issue of ego was mentioned. God in a sense was saying ok, you guys think you can do it yourselves, then keep all these requirements. The law was to show them their weaknesses and limitations and to set a standard they would need to keep in-order to be righteous before God. However they failed time and time again. Your second point did Christ's sacrifice work? Yes, but the next question is how? God now looks at Christ for the fulfilling of the law and it's requirements and not sinful man.