From the RIAA's point of view, it works to their benefit that a download link doesn't exist, and it may be something they like, but that doesn't mean that's why.
It could just as easily be that a download feature doesn't exist because YouTube wants you to keep returning to their site if you want to rewatch a video.
It would be one thing if some YouTube videos had a download button and others didn't. That would suggest that, on the ones where it's missing, it is missing for a reason, and that reason might be DRM. But as far as I know, YouTube doesn't have download for any videos.
Software doesn't always have all the features that end users might want, and the mere absence of a feature doesn't necessarily tell you why it's missing. Also, it's not some weird, suspicious thing to write software which fills in a feature gap in some other software. (Google encourages add-on software on other products, too. For example, Chrome extensions and Gmail add-ons.)
But, maybe there is some legal reason why this could make sense. Maybe some terms of service or licensing (for video uploaders or for regular end users) says not to download something, which would make it clear that the download feature is missing on purpose.