Now after the internet has taken over a substantial part of shopping, I am interested to know the current trends in the traditional retailing industry. How is it adapting to compete with mature online shops?
It depends on the segment. Some segments like bookstores are being completely replaced by online versions and they are going out of business. Some like garment and sports stores are coming up with hybrid models where they keep the brick and mortar shop and at the same time have extend them with online shopping. This is what is most commonly happening.
Finally there are segments that are untouched by the internet. Online grocery shopping has proven to be failure and most groceries, corner shops, hardware stores are doing business as before.
All business can utilize the marketing opportunities the internet brings by having a web presence and doing online advertising to reach customers they previously couldn't.
Embracing it is the only way to go.
Services such as amazon allows all vendors to sell to (in this case) amazon's customers, but also allow you to pull in data from amazon and make your own .com site which can choose to use amazon's payments and fulfillment services.
More info: Second time today I post this video (for different reasons though): http://www.infoq.com/presentations/vogels-amazon-platform (at the start it shows a glance at how to use amazon for your own retail)
To answer your question directly: It is not a competition anymore, it is cooperation which in fact benefits a single retailer much more than it does amazon (so go for it). Amazon only benefits from all the retailers put together.