Hi,
To get the best performance of your server, please check and apply suggestions from this documentation. That will help you maximize the plugin performance. I specifically recommend using the Index Table engine, that can make a huge difference.
The search used on the linked website is a high performance custom built search engine for that specific project. There are some plugin capable of almost instant search results – but the pricing of those are way beyond of this plugin (usually from $600 a year for the lowest subscription tiers). With this plugin there are no yearly fees, however the performance is limited to your local server performance.