There are search engine libraries out there that they could link into the thing. Like, if you asked me to build something like that into a small website, I could probably get some kind of search functionality working reasonably well inside a week.
But...Reddit isn't just any old website. it has to scale pretty well. Reddit has a lot of text to search through. Reddit has new content being constantly added that has to be added to the index at a pretty rapid rate. Reddit permits comment deletion, which means that the search engine's index probably needs to support efficient deletion of arbitrary comments from the index, which I suspect is fairly uncommon for a search engine (and which many index designs won't handle efficiently). And a search engine used by Reddit probably needs to support some kind of architecture for running a distributed set of search engines and generating and distributing index updates reliably, which is something that Ye Typical Search Engine Backend probably doesn't need to deal with and may not have support for.
But if you type "reddit <whatever you're searching for>" into Google it shows up instantly.
Google put a lot of (expensive) engineer hours into building that kind of scalability. I don't know what kind of money Reddit pulls in, but I can guarantee that it is nowhere near what Google does.