The trend is coming indeed outside gaming. It is a mix of psychology and ranking (but ranking is also based on psychology). So the short answer is it is psychological trick.

If to talk about which game first used colored tiers/ranks I think it was FF, but I might be wrong according to this article:

Diablo:

The first game's division between standard (white) items, enchanted (blue) ones and uniques (yellow), may be considered an Ur-Example. The sequels add the green "set" category, where items from the same set are more powerful when used together, and gold or orange tier for uniques, while yellow items become a more powerful tier of "randomly enhanced" blue items.

In case you'd like to learn more without going too deep in psychology there is a Wiki article (very brief and simple version of psychological effects of colors). For deeper and more exact knowledge, I'd recommend to study psychology and philosophy (at least to read a textbook or attend several lectures in some college or university).

The Meaning of Colors

While doing research on why the color-coded system came to existence, I remembered that each color is perceived to have a few meanings.

Looking at this list, there could easily be some links to why they picked certain colors. For example, in Star Wars the Old Republic, the ordering of items is White (standard), Green (premium), Blue (prototype), Orange (custom), Purple (artifact), Deep Purple (legendary), Light Yellow (legacy), and Yellow (mission).

The Purple and Deep Purple items are very rare and powerful, which could easily be traced back to the meanings that purple has, sophistication and power.

Besides just this, these more rare and vibrant colors pop out more, and are more likely to draw a players attention. Mix this with making them rare, and these exotic and new colors will easily grab a players eye while they are playing as they are rare and new.

Color Psychology

Gaming History

Going from the history of gaming and seeing where it was used, an early contendor is Diablo 1, which came out in 1997. However, the best contender I could find for setting the trend in motion early was Diablo 2, which came out in 2000. Here they used a myriad of colors to clarify between different types of items.

They used White for Normal items, Blue for Magic items, Yellow for Rare items, Green for Set items, and Gold for Unique items.

Which is easier to see in a gloomy crypt, a dark gray glow or a bright yellow one?

After Diablo 2, World of Warcraft (released in 2004) was the next major game that I could find that started using color coding for it's loot system, and it was very easy to see it was based off of the Diablo 2 coloring system, which is the same for every game that uses the coloring system. Gray for junk, white for common, green for uncommon, blue for rare, purple for epic, orange for legendary, gold for artifact, and cyan for heirloom (with the latter two only being added in later additions to the game).

While Diablo 2 started the trend, I think it would be safe to say World of Warcraft really set it into stone.

Note: Both of these games were made by Blizzard Entertainment.

Non-Gaming History

Outside of gaming however, color coding based on value or rarity probably dates back a long time. Just one that is coming from the top of my head is the color of coins. Gold coins are made of a valuable metal, meaning a gold coin would be worth more than a silver coin. While this is not directly making lists based off of value, the value of the coins made their own color list, associating gold with value and silver with less value.

Coins in the Byzantine Empire

I refer to both the Solidus(gold coin) and the Follis(silver coin).

Much like the coins, indigo was another instance of color being related to value. The dye itself was rare in Europe at one point, so the mere use of the color dictated value. It might just be a color, but because it was different and rare, it had value.

Indigo Dye

Conclusion

There are multiple reasons to why I believe colors are used to denote rarity in games.

• Unique colors stand out: on an ease of access standpoint, developers would choose colors that stand out somewhat and grab players attention, so they do not miss them.
• Colors have meanings: with colors having meanings, different colors would subconsciously associate with how society has formed them. Purple being rare and royal, while gray being bland.
• Consistency: once it was solidified by Blizzard in Diablo 1 and 2 and World of Warcraft, all of the other games that would use similar loot systems probably followed in suit. This would make the games friendlier to players who were coming from the Blizzard games. Even though some companies would make changes, they would remain generally similar.
• Colors Have Had Value: Even though coinage does come with some real value tied to it (gold physically being worth more than silver), it still has been shaping society to understand that gold is more valuable. The same is for indigo.
• Scarcity: The rarer items are usually the ones with colors that was once considered valuable, such as gold or purple, which could be a reason to why they are used for valuable items commonly.

Simply put, the color rarity system was re-adapted for games by Blizzard Entertainment with Diablo and World of Warcraft. As a basic concept however, it has been around for a while. It is all balanced deep in the human mind, and how we perceive colors and how scarcity works.

The other answers mention the origins tracing back to Diablo. According to Diablo designer David Brevik (on the May 16, 2019 Game Informer show):

Angband was a game that I played literally thousands of hours of ... there were different random items that you could get in the game and they had different colors ... if you found a rare one the text wasn't just gray it was blue text and that meant it was like magic ... we expanded on it but originally the idea came from Angband