http://www.domainsbot.com checks way more than 10,000 for every search, doing semantic matching. They have been doing it for years.
I'm sorry but I'm failing to see how this is cooler other than the fancy colors.
But the fact that LDS employs a strategy that consistently results in catchy-sounding, hyphen-free and available domains does differentiate it.
Not to knock domainsbot.com, they do have killer matching algos under the hood (as you mentioned), I don't believe they have false-positives (rarely if at all) and they bring in aftermarket domains to results, but from a starting point like "game", I only get 2 suggestions in the .com namespace (no hyphens, permit related keywords, suffixes and prefixes).
LDS on the other hand brings back 54 domains. I'm not saying all of them are gold, but I would certainly consider "gamegroovy.com" for a gaming related site.
This is likely the case for many other popular / high-value keywords, eg. cloud.
I think that branding is an exercise that requires a lot of creativity supported by a range of tools. LDS is very strong in its techniques.
