At first glance it would appear that the question is preposterous, rather ridiculous, there is no chance that a house pet being trained other then being a pet could be a symbol of enslavement to its human counterpart.
Then again, it's an intelligent question, more philosophical and in this time and age a more contemporary question than it ever was before.

Unfortunately, yes this is my opinion and I am aware of it, there isn't a true or false or a wrong or right to this answer. Yes, animals are being held as slaves to do labor, ever since humanity thrived as a collective being, and up until today every animal has it's own destiny to fit mankind and be exploited of.
What's really hard to tell is, if house pets also function as slaves do? They have been trained and have been living with humans for so long, not to mention the breeding of other animal races, which leads a lot of mixed breeds to only survive alongside a human. If there weren't a human, their lifespans would drastically decrease and it would only be a matter of time until they either go extinct, or the positive part, evolve through evolution and become the wild beasts they once have been millennia ago. Here I am mostly talking of dogs as house pets, but cats are also victims of human breeding engineering, while cows and hens might also be too domesticated to live in the wilderness without being too abundant of humans.

The negative point of view is, yes house pets are enslaved animals that are used for human purposes, be it to comfort them (humans) physically or be there for them emotionally.
The positive point of view(s) is, that there is no scientific proof that they are aware of their current state. There is proof that animals are intelligent, and that cats do not connect emotionally to humans like humans do the other way around, but rather use humans to be worshipped and fed and be petted(Ancient Egypt and Modern Age). Cats are aware that they will get what they want, while dogs show their affection to humans and also show humans that they are physically (food) and emotionally (need to be petted) abundant. To add more solids to my arguments, there are scientific proof that animals mostly react through instinct, that they do not perceive past as humans do. That leads us to the conclusion, that house pets would only be aware of their "enslavement", if they had the processing power to think about the past and think a lot of it over and over again.

My opinion is, it is sad to admit that yes, they are slaves to mankind. But, they aren't aware of it, and second, they are treated like first class customers, heck, even better than some humans get treated on earth.
For example humans tend to debate about why a police dog gets cheaper food a day than people do on welfare. So, what we need to do as humanity is really, get things together and start treating all animals alike by stop exploiting them (for example: cows and chickens). I also do recommend you guys reading Animal Farm by George Orwell, in which animals have gained a specific type of intelligence and work together to overthrow human tyranny.

That's all from me... A bit too much to read, lol if anyone wants to.

Thank you @lesliestarrohara for this lovely mind-opening question.
I also need to know, are you a vegan or not? It doesn't matter to me, it's just a wise question you've lit the fire with, and interesting for me to know if you are or not.

• Cheers