Sometimes when you go to google search, it will prompt you to download the their app, download chrome, use their native weather, news, etc. It is part of how they iterate on their core search product. If they decide to show Google shopping, isn't that their product decision?
Yes, it is. The problem comes in when a company which controls a significant percentage of one platform (search, in this case), uses that advantage to muscle in to other areas.
This is seen as a bad thing, because beyond the consumers are left with an unbeatable giant. Unlike normal market leaders, however, this giant doesn't need a superior product, but only apply leverage (given by their other positions).
This is the very essence of anti-trust / monopoly laws. Competition is a good thing.
If you're not a monopoly, you can do whatever you want.
Things change when you are a monopoly - ie. you have more than 50% of market share (maybe it's more than 50%, I don't know EU threshold) - then special rules apply - in general you can't use your monopoly position to control other markets.
Prompting to download Chrome may be against EU law. They could give a list of modern browsers if detected an old one for example. I actually don't understand why are they not forced to change it just like Microsoft was few years back?
This law is in power to avoid single company gaining total control.