memes

You just explained the connotation and presented it as a difference in definition, but an ultimatum is just attaching consequences to a "hard boundary" or "deal-breaker." Usually, the consequence is just walking away from the relationship. I know in real life it often does turn abusive, and you can have an abusive ultimatum, "have sex with me or I will hurt you," but it's not inherently abusive.

Even your examples are ultimatums but said more kindly.

“I feel neglected when you play video games so much instead of spending time with me, what can we do to find something that works for both of us. If we can’t find a solution, I worry about the sustainability of our relationship”

The boundary is "being in a relationship with someone who plays video games so much" and, assuming the status quo is not acceptable, what turned it into an ultimatum is "I worry about the sustainability of our relationship." I.e., I'm going to break up with you if you don't play less video games than you are now. Just because you would like to stay in the relationship and keep playing video games at the same rate does not make it abusive. What would make it abusive is if there's a pattern of manipulation that puts the ultimatum in a negative context.