(NASDAQ:AMZN) recently kicked Apple's (NASDAQ:AAPL) digital streaming box, along with Alphabet's (NASDAQ:GOOG) (NASDAQ:GOOGL) Google Chromecast streaming stick, out of its online store.

The move comes right when all three companies have updated their streaming devices just before the critical holiday sales season. It's a clear attempt for the online retailer to increase sales for its own Fire TV and Fire TV stick products at the expense of Apple TV and Google's low-cost USB-dongle media player.

It's not an unprecedented move, but it's a rare one for Amazon, which is staying in business with its two rivals for other products -- even tablets where iPad and Nexus devices compete with its Kindles. Even though Amazon is firing this shot, one could argue that the war was started by Apple and Google, since neither Chromecast nor Apple TV offers Amazon's Prime Video app.

That's a telling thing, because will still be selling Roku's streaming players, which control more market share than any other company, according to an August report by Parks Associates. The online retailer cited the lack of Prime Video as a reason for stopping sales of the two devices in an email it sent to sellers.

Source: Parks Associates.

"Over the last three years, Prime Video has become an important part of Prime," Amazon said in the email. "It's important that the streaming media players we sell interact well with Prime Video in order to avoid customer confusion."

You can see the logic, especially when you consider that Prime members spend twice as much with the retailer compared to users who do not pay for the $99-a-year service. Still, dropping Chromecast and Apple TV could lead to reprisals from the two companies toward Amazon and it will cost it some revenue in the short term.

How much will it cost Amazon?
Chromecast and Apple TV are both top-selling devices and if Amazon does not stock them, people are likely to go elsewhere to buy them rather than substituting a Fire device. Dropping the two devices could cost Amazon significant sales over the next year, according to research from 1010 Data:

Through Amazon alone, Google and Apple did about $85M the past 12 months. Factoring in growth and the likely continued popularity of these devices, Google and Apple could easily have done over $100M in sales of streaming TV devices on Amazon over the next 12 months.

That sounds like a big number, but in reality the loss of Amazon as an outlet may be worse for Apple and Google than losing the sales will be for the retailer. According to 1010 Data, both companies are heavily reliant on

What does this mean for Amazon?
In the short term, the loss in sales barely impacts Amazon's bottom line, but hurting its relationship with the major companies could come back to bite it with consumers.

"This has the potential to hurt Amazon as much as it does Apple and Google," Barbara Kraus, an analyst at Parks Associates, told Bloomberg. "As a retailer, I want to give people a reason to come to me. When I take out best-selling brands, I take away those reasons."

While its logic is sound, when it comes to Apple TV and Chromecast, Amazon is also taking a risk by pursuing this strategy.

"Fewer than 20% of Amazon customers are Prime members," Wedbush Securities Analayst Michael Pachter told Bloomberg. "What about the 80% who want an Apple TV to stream Netflix? I think that the excuse of avoiding customer confusion is a not-so-veiled attempt to favor Amazon first-party products over third-party products, and think it was a bad move."

Amazon is clearly trying to flex its muscles and get Google and Apple to include a Prime Video app. That type of tactic has worked for the retailer in other disputes, but it may not work in this case. Roku, for example, has to kowtow to Amazon, but Google and Apple have considerable distribution power on their own.

In addition to potentially angering shoppers right now, Amazon also risks Apple or Google pulling whatever the next hot, new device is from its shelves or offering it on less favorable terms.

This is a game of retail chicken and it's hard to see how Amazon wins in the long run. The retailer may be able to push around publishers, which need it as a distribution channel, but Google and Apple don't. That's not to say they won't be hurt by this, but so far it's a game where everyone, consumers included, loses.