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I did it! For anyone who has a similar problem, when using custom classes in HTML and CSS always remember to use custom- before the name of your class. 

So for me this did the trick:

<div class="custom-embed"><iframe loading="lazy" src="[put your source here]"  
style="border:0px #FFFFFF none;float:right" name="browserGame" scrolling="no" frameborder="0"  marginheight="0px" marginwidth="0px" 
height="210px" width="310px" allowfullscreen=""></iframe></div> 

And then in the custom CSS editor:

.custom-embed{float:right}