A great example is Gumball. Gumball does internet-era comedy in a way that still works on its own. Trendy vernacular is used sparingly and believably (though it can still be jarring hearing terms like "baller"). It also references specific internet phenomenons and viral videos instead of drinking from the meme fountain. See here:
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There's an entire episode, The Uploads, that nails "YouTube culture" in its entirety. I recommend checking it out if you want to see "internet humor" done well, even though I don't think it's that great of an episode in its own right.
Gumball I always saw as the kid version of Regular Show but with varied animation, they use everything and it stands out.