When DogeCoin was first created it was a simple Litecoin Clone, it offered no new features, such as increased security, or rarity, or hosting domain names, or alternatives to mining. It offered nothing new in terms of technology. But DogeCoin did offer 2 things that other coins did not offer.
First and most obvious, it provided memeability. With phrases like so coin, much wow, very money, and other phrases like that, it was easy for someone to randomly come in and join the community simply by posting a funny phrase in a thread or creating a meme, which gave the coin value. The memeability of the coin also helped it spread quickly to sites like 4Chan and eventually Facebook and Twitter. All of which increased the value of the coin by bringing new users and new buyers.
But the second factor is not so obvious and you had to be there when DogeCoin started in order to recognize what happened. When DogeCoin started the people mining the coin were getting so many coins (tens and hundreds of thousands if not millions) that they were just giving them away. DogeCoin started with a value of 0, so people would give away a hundred thousand coins at a time without a second thought. Then the value increased, so in the give away threads they started telling people to post their wallets and they would give them 10,000 DogeCoins. And they did. Then the value went higher, and the give away threads lowered it to 1,000 DogeCoins. Until eventually it got to the point where Bitcoin is where people just opened faucets and gave away 10 coins or 1 coin at a time. The give aways increased trade volume, and because both trade volume and new adopters were increasing at the same time, the increased trade volume had a positive effect and not a negative effect. The more people that knew where to get free coins, the more thcoins would show up on exchanges, then as the memes spread the more people who saw the memes but did not know where to get free coins, or wanted to have larger amounts to trade back, would buy the coins on the market. And as all of this happened the people who had Bitcoin ready to spend went and bought DogeCoins with their Bitcoins, knowing that they could trade them back later for more Bitcoins than they spent.
When DogeCoin started it wasn't just the funny Dog and misspelled words or people saying: To the Moon! that gave it its value, it was the spirit of the community, giving away free coins just so that more people could say "I have some DogeCoins". That is how DogeCoin overtook so many Cryptocurrencies basically over night.