The initial Yu-Gi-Oh! card game featured a more simplistic format. It went through an evolution phase in the last few years, where we saw the introduction of Synchro cards, XYZ cards and, most recently, Link cards. These did not previously exist and complex special summons in the older format consisted of fusion and ritual summons. The older format featured longer duels, possibly more powerful cards and is evidently more representative of the classic Yu-Gi-Oh! anime and those that followed shortly after, such as Yu-Gi-Oh! GX. Most children who have watched the original anime and/or Yu-Gi-Oh! GX would be familiar with how the older format of the game works and would subsequently be able to play the game either in real life or electronically. I recall playing Yu-Gi-Oh! Power Of Chaos when I was 6 years old, and I still play this game occasionally today.
The introduction of the above-mentioned cards and the substantial changes that were consequently made to the game format, combined with a growing (age and number) audience, has rendered Yu-Gi-Oh! a more complex card game, making it suitable for older audiences. Additionally, note that there was historically a significant number of older players attending and participating in Yu-Gi-Oh! tournaments.
I personally don't like what Yu-Gi-Oh! has become, and I prefer the older (pre-2008) format to the newer (2008 and beyond) format.
I hope this helps!