At this point, core 2000s culture is gone, and elements of 2010s culture is starting to come in. But with that said, it was still mostly the 2000s. Here are some bullet points of which aspects of this era are 2000s, and which are 2010s.
2000s-Feature phones were still a common sight to see.
-The Wii was still very popular
-The rhythm game craze was still big. Local multiplayer in general was still a thing.
-Portable gaming was still mostly centric on consoles rather than phones
-YouTube was still old-school, pre-HD, people still found FRED and Spaghetti/Dinner YTPs funny.
-As nightmarefarm pointed out on another thread, the 2010s didn't begin politically in the UK until David Cameron.
-Glossy skeuomorphic aesthetics were everywhere
-Though declining, MySpace was still very common to see, most YouTubers still linked their MySpace during this time for example.
2010s-iPhones and smartphones in general are increasingly becoming more common
-Early emergence of modern casual gaming with the likes of Farmville and Plants vs Zombies
-Minecraft got its start here
-The MCU already had two movies by this point. Superhero movies were a lot more popular than they were even in say, 2006, for example.
-Electropop is rapidly rising in popularity, as is dance music in general.
-Not much rock on the radio by this point, and most of what is on the radio sucks ass
-Barack Obama was president