I think that’s a pretty good definition. Maybe more specifically, it’s generally only applied to organisms, although examples used to support the idea that design is detectable are taken from other areas. How would you define it?
No it's not.
That's exactly what it is, in technical terms. Anyone can read the leading works like Dembski's The Design Inference to see this is bluntly the case. People need to understand that opposition to ID is literally a denial of the existence of engineers and factories. And there are plenty of in-context quotes from Darwinian fundamentalists that, applied consistently, prove this.
Someday some rogue scientist is going to engineer a pathogen and release it. And the NAS and other evolutionary fundamentalist organizations are going to quickly declare that it is illegitimate to believe the organism was modified by an UNKNOWN INTELLIGENT DESIGNER, because that would be "religion." At least, that would be the case if they are consistent.