No, we need to make that more clear on the site. It's our own search engine, written to overcome some of the limitations of Lucene. In particular, update of relevance formulas on the fly so you can experiment without reindexing.
But most importantly, you don't have to deal with installing, configuring, managing and scaling a sphinx setup. IndexTank is cloud-based, you don't have to deal with servers, RT indexes, hadoop, and so on. We worry about all that.
I had a thought that relevance should be computed like a "stream database", but with an index rather than a data store behind it. Maybe something like Streambase - but written in Clojure - on top of the lucene index.
Take it one step further, where the entire index is expressed as s-expressions (i'm a bit out of depth here) - you can basically write a mapreduce job on the index.
However, I'm not so sure that computing relevance can be parallelized - i.e can it be broken down as opposed to be computed as a global problem ?
http://indextank.com/documentation/function-definition
(Feedback on this documentation is more than welcome, it's a work in progress!)