I didn't write down the name of the person who made this comment (on a different discussion) about the difference between "spiller" and "leger":
"Spiller is playing structured games like board games, or sports, while leger is more like free play outside, running around, or what animals do."
There are a lot of words with "ej" in them that are also pronounced "eye". I am just a beginner but can think of two straight away: "stej" (roast) and "spejlæg"(fried egg).
The "g" in the words "leg" (game) and leger" (play) is not pronounced. Think of the English words "lie" and "liar" and you will get very close :)