Oh thanks for letting me know. This is the waffle maker I've had for well over 5 years now and it's still going strong: https://amzn.to/3BRsT7t (affiliate link)

It sounds like something went wrong here for sure as this recipe is a really popular one and generally gets good feedback. I make them myself all the time too.
I have never used rice milk but as long as it's the same texture as other plant-based milks it should be ok. If it's really, really thin then it could have contributed to the problem.
The batter shouldn't be pouring over the sides of the waffle iron. You need to stop filling the iron before that happens. All waffle irons are different sizes so you need to adjust the amount of batter used to suit.
Did you use a different flour than the one stated? That can greatly affect how a recipe turns out. These waffles have only been tested with spelt flour.
Also did you weigh the flour or use cup measurements? Cups are not accurate enough for measuring flour and it's really easy to get not enough or too much flour in the cup. The only way to be accurate when measuring flour is to weigh it.
I hope that helps!

Breakfast for dinner is never a bad thing! ;O) I'm really pleased you enjoyed them. I have lots of other pancake and waffle recipes too so you won't be lost for ideas. My Banana Pancakes are the most popular. They are so thick and fluffy! https://avirtualvegan.com/vegan-banana-pancakes/

Thank you so much Danny. I'm glad you and your family are enjoying them!

The oil really makes a difference to the texture of the waffles. They become much fluffier with it. You can omit it if you don't mind them losing a little fluffiness. They will also be more likely to stick in the waffle iron without the iron so keep that in mind.