I am looking at the different ways in which FX options (say EUR/USD option) are quoted in interbank markets. Is it quoted using the option chain? I also saw a piece where it is said that it is quoted based on implied volatilities. I am a bit confused here. Is option chain only quoted to retail investors and not in the interbank market?
You are confusing listed options with OTC (over the counter options). Conventional option chains only exist for listed options. Equity and commodity are liquid listed option markets. FX and IRS are predominantly OTC markets and mostly volatility quoted.
Focusing on FX, there are listed option markets as well. The CME offers both, vol quoted and premium (price) quoted FX options. These options are on futures though, as spot FX is not exchange traded, meaning you have options chains, based on listed future contracts. There exists the concept of triangulation between the 3 books - Premium quoted options (PQO), Futures (FUT), Vol quoted options (VQO). Applying Black 76 (because its on futures), one can manually convert (provided one uses the same interest rate as the CME) the volatility to the premium provided by the CME.
The CME link above has a informative video for the so called CME triangulation and why vol quotes make sense. The 2pm expiration time mentioned in the video is the cut-off of the product (time it expires). Essentially one trades in volatility, but clears in premium.
Leaving listed options aside, OTC is almost always vol quoted. With regards to FX, Uwe Wystup wrote numerous papers and books that explain almost every nuance of FX trading. There are various SE questions like this one.
How the implied vol quotes combine to a full vol surface is explained here. In reality, there are numerous details and I recommend you to read the paper FX Volatility smile construction by Uwe Wystup and Dmitri Reiswich. This answer has a screenshot of the various delta quotations that exist. Iain Clark's book Foreign exchange option pricing explains why the choice of delta is sensible, as discussed here as well.
The fx interbank option works by dealers quoting standard runs of implied volatilities on specific tenors and product types (fly/strangle, risk reversal and at the money) which are currency pair dependent. The strikes that make up these structures are negotiated as part of the deal. Some market data providers publish these implied volatilities (like Bloomberg) but implied vol is king for vanilla options interbank.