What do you mean by bandwidth exactly?
They are storing reviews and profiles in some persistent storage on the backend, such as a regular relational database. They index certain fields in certain tables, just like you would normally with a database. They don't store any pics/binary data obviously, so basically it's database full of tables of string/text fields.
Elastic is essentially another type of database. You index documents and store them. Then you retrieve them. Instead of 'schema', you have mappings. You have fields that have built in analyzers
Full text search is possible in both. Is it 'expensive' in both? Yes. But if you know which field customers will search by, it's not that bad.
So, elastic is something you run on your backend, just like a regular database. It probably does take more resources than a compact db, but I don't think it's a big difference. Usually if you need to update fields often you'd choose a regular db, but if you mostly insert and retrieve youd use something like elastic or a kv store.
Part of the reason elastic is good is exactly because of the built-in text analyzers for text fields. Elastic is often used for logging. Writing logs to files is super expensive and you need to manage those files and searching through huge files is painful. Searching through elastic is great and you'd usually index each day of logging so you can delete old indexes you don't need.
The problem is, migration can be painful. Although, with only 2.5 million entries of reviews on TER that aren't updated often, I think it's quite manageable in 2020. However if they have a separate table for girl profiles and they have relationships, things start to get murky fast.