Do these kind of games have marketplaces?

Destiny for sure has no trading, can't remember if the division did and I haven't played a diablo game in ages.

Blizzard tried this sort of thing with the Auction House, didn't they? It lasted about 1 year and they were forced to remove the feature in South Korea after it was deemed illegal 

The Division has trading but it's very limited.

You can give a loot drop to another player if they were in your party when it dropped.  The ability to do this lasts for twelve hours.

The point of a game with a loot emphasis is to keep players playing to get the loot, so they have an incentive to make it hard for you to just buy stuff from other players.

After extensive discussion wanting 'text chat' to be a thing for ME3, DAI and MEA, it never happened.
Was this a thing in Destiny / The Division? I've played both of those and don't recall it.

Destiny 2 (pc version) will be adding chat text at some point. Good luck getting console to do it cause most people don't like it (I wouldn't either, using a controller for chatting sucks compared to a keyboard). 

Warframe has a trading system using text chat to communicate bids or offers (WTS/WTB). The items that can be traded are restricted (prime parts, prime weapons, prime sets, special mods, etc.). Prices are quoted using the main game currency - Platinum. Items can be sold for Platinum, or traded for an equivalent item. This system makes it easier to get specific parts you need without grinding RNG forever. It also means you have a way to earn Platinum without paying real dollars, although you can buy Platinum if you want from DE directly. (Warframe is free to play; you are not required to buy any Platinum to play the game.) All trading must take place in a clan dojo, so this system encourages players to join a clan so that they can trade.

Overall, the Warframe trading system is a pain to use: the text chat is hard to see, bids are mixed with offers, there is a huge list of tradeable items that is not organized by category, prices are a total guess, noobs get fleeced on pricing, and many times there is no response to your offer. You can waste a lot of time trading in Warframe. Despite continued complaints in their forums, DE has no plans to improve the system or make it easier to use. Despite these issues, the Warframe trade chat is going strong after 4+ years; it is very busy on a Saturday night, although there seem to be a lot more sellers than buyers.