There's two big things that may help with keeping things fun.
On the Floor
First of all, think of the Colosseum. While when people think of gladiatorial combat, they tend to think 1v1 duel to the death or man vs beast, there would be far more going on than that in an actual arena. Yes, you would have that, but you would also have acrobats and magicians performing routines, chariot races, and stage plays. Foot races, swimming races, and other sporting events. And if your king wants to really pull out all the stops, you can do what Domitian did where he somehow flooded the Colosseum and staged a naval battle.
All those things were done in a world without magic. There's no requirement that your players only compete in the arena. Who's to say a wizard among them wouldn't also be drafted into pleasing the crowd before the individual bouts? The same could be said about rogues and acrobats. Someone got a particularly high CHA score? Maybe they're a comedian or an actor!
Even on the floor itself, you can make things exciting during "traditional" combat. Why not add trees on carts to give cover? Why not allow the whole party to sometimes compete together and face off another band of criminals so they can learn the value of teamwork in D&D?
If you're cool with homebrew, you might take a look at this idea of turning Witch Bolt into a dueling spell. It might not be right for your world, but I guarantee watching two wizards go at it with a genuine dueling spell would have the arena's crowd spellbound (pun very much intended).
Variety is the spice of life, so as long as you go big (and since they'll eventually be granted a chance at freedom by the king himself, it sounds like you can), you shouldn't have any difficulty keeping what's happening on the arena floor itself interesting and fun.
Off the Floor
The other thing is that what goes on on the floor is only a fraction of the whole gladiator lifestyle. Clearly, it's the exciting part, but it's not the only part. Suppose immediately following a bout, the victor(s) get to make a victory lap during which the crowd is free to donate coins to the cause. Now your gladiators have a source of income they can use to buy better gear, bribe guards, and secure niceties they might not otherwise have.
Now that they've got an income, what if they were allowed to place bets on the victors in NPC fights? What if they could surreptitiously interfere with future opponents, fiddling with their gear to make things go in their favor?
What about the social dynamics of getting in line for the daily slop? Those perceived as the best or strongest and those they like might get the front of the line while others find their way toward the back where they'll get less food and it'll be colder. Does your party band together to try to collectively bargain for a higher rank in the line? Does the tiefling barbarian muscle his way through and the gnome he's friends with follows in his wake? Does the silver-tongued halfling rogue just talk his way to the front of the line? Does the particularly charismatic fighter who receives an unfairly large sum of money from the crowd just bribe her way to the front?
What about practice? Gladiators didn't just randomly get pulled out of cells and tossed into the arena (obviously some did, but not all, and certainly not those that made a career of it, which yours effectively are, it sounds like). You could allow them to train against each other with nonlethal weapons, still giving them experience without putting their lives in danger. This would also give them a chance to show off their skills to the other gladiators. Maybe a few NPCs will become sycophants to your party. Maybe one might even get released alongside your party and join them or others might show up later in their quest after securing their own releases.
Maybe there's already a dominant gladiator in their cell block with a following. Do the PCs beat him into submissions? Kill him quietly in the night? Bribe him? Join him? Convince him to join them? He could even effectively be the Big Bad for this part of the story if that's something you'd like, a way to give it an overall arc without really impeding the rest of the story or preventing it from progressing forward. Maybe beating him and his goons in the arena is the final battle that gets the king's favor?
Whatever you do, just make sure to keep things variable and make sure the players are doing more than just fighting increasing numbers of goblins. There's a ton you can do on and off the floor to keep their lives interesting, letting them learn about the game at their own pace, and giving them clear goals to work toward.