There're a bunch of cultural features that tend to prevent internal competition at Google:

Everybody has access to (nearly) all source code. The single repository means that you can dig in to find & fix problems in any Google product, regardless of your position in the org chart. And if someone invents a feature that you want to use, you can just grab it, like the appearance of Wonder Wheel on YouTube.

Google has a strong ethos of "If it's broke, fix it", regardless of the org chart or assigned responsibilities. It's usually mentioned to you as a Noogler, but what really reinforces it is the reaction you get when you actually fix something broken. In a lot of companies, there'd be a bunch of "Who is this guy and why is he mucking with our code?" recriminations (if you can even get access to the code). In Google there's a "thanks for doing this" and sometimes a peer bonus.

Code reviews help a lot, somewhat paradoxically. When all code is reviewed, you lose the fear that you'll break somebody else's code with your fix. You make your fix, send it off, and if there're problems they'll have you fix them in the review. If it conflicts with the overall goals of the project, they'll just deny your patch.

In a system without code reviews, chances are that you'll break something by contributing to a project that you don't really know about. And once enough people have broken things, the company institutes code ownership policies that mean you can't fix things in other products.

There's also 20% time, as someone else mentioned. And the combination of free meals and pretty fluid inter-project mobility. It's likely that your teammates have worked on other projects before, with people who are now in wildly different areas of the company.

Finally, there's just the difference in growth rates between the two companies. Everybody at Google has more work than they can reasonably do. If somebody else does the work, it just means you can go home early this week, and there'll be plenty of other things to accomplish next week. If you spend 3 months writing a dialog box in Windows, though, and somebody makes that feature obsolete...well, that rather sucks.