MeiliSearch appears to be more of an alternative to Lucene than it is to Elasticsearch. Lucene is the search engine that runs on a single instance; ES is the horizontally-scalable distribution and aggregation layer atop the instances. Absent a similar aggregation layer, MeiliSearch isn't "elastic" as the comparison implies.
Actually Lucene is the library for search that Elastic uses under the hood. Lucene does not provide any HTTP API, which Elastic does. Before using Lucene, you have to build the interface around it.
In this way MeiliSearch is comparable to ES, especially for site search and app search working out of the box as standard with its http api.
MeiliSearch does not offer distribution yet, but it is something the team is working on :)
My concern is that by comparing it to Elasticsearch, you implicitly minimize the amount of engineering effort required to go from single-node to a distributed system. It is a non-trivial exercise that you will undoubtedly realize once you get into the dirty details.