Never played a Yu-Gi-Oh game.
Tell me, how does it play?
It's a trading card game - if you've ever played Magic or Pokémon TCG, it's similar to those. Basically, you collect cards, build a deck, and play against opponents. You win money by defeating opponents, which you spend on packs of cards.
There's ~5500 unique cards in the game, so there's a ton of options for deck building. A lot of the fun comes from trying out new combinations of cards.
The actual battles are turn-based; in your turn, you summon monsters, play spells, set traps and attack your opponent; in your opponent's turn, you can use the traps you set to hinder them. The aim is usually to reduce the opponent's life points to 0 by attacking (some decks can also win in other ways, such as the ever-popular Exodia card). The AI is pretty decent, if a bit slow (hopefully the 3DS's faster processor will drastically cut down how long the AI takes to make its moves).
Once you've collected enough cards to make a good deck, you can play against people online for a bigger challenge.
The advantage of playing a video game version over the physical card game is that you pay your $40 (or however much) once, and then you can unlock every card currently in existence for free by playing the game. In the physical card game, you buy cards for real money; Konami usually makes the powerful cards very rare (you might expect to find a single copy of a sought-after card in a hundred packs), so it's
way more expensive to play the physical game. It's not unheard of for good cards to cost you nearly $100 per piece (and you might need up to 3 copies!).
Is the show still popular? Or could it be that I missed someting and Yu-Gi-Oh as a video game series has evolved and gathered a huge following.
Last time I played a Yu-Gi-Oh video game was like 13 years ago, Forbidden Memories on the PS1, haven't heard anything about the newer games. :/
Anyway, a TCG game on 3DS is always something to be interested in because the system lacks those.
I don't know about the show, but the physical card game is still one of the most popular TCGs along with Magic and Pokémon. We still get new set releases on a regular schedule, and thousands of people turn up to tournaments. I don't play anymore myself due to cost (see above), but the video games are a good and cheap alternative.