Talk to Your Players
Almost every answer here is going to suggest you talk to your players. If you take nothing else away from this, let it be that you talked to your players. So what are we talking to them about?
Expectations can be a powerful thing in life. We often regard the outcome of things with relation to our expectations rather than an objective account of the results. Put simply: When expectations are met, people are happy. For example, even a bad movie can result in a good experience if you expected it to be worse than it was. More to your issue, you don't want to manage the expectations of quality, you want to manage the expectations about what your game is about. At the start you need to make sure everyone is on the same page. Talk to your players. Talk to them together! Have a session zero in which all of you discuss the type of campaign you'd like to play, the setting your players are interested, what characters they'd like to play, and what rules you want to follow. I've had just as much fun talking about the session we just played as actually playing it. This session can similarly be fun and educational. You don't need to have a campaign set in stone by the end, but use this session to manage expectations and get information. After that, Define a concrete style of game and make sure everyone knows what it is before the campaign starts. This can be done in the days/weeks after session zero, but when the campaigns starts, let everyone know what your goals are. How much ammo are you counting? How much time do you want to spend in town? How much role-play are you going to strive for? Do you expect players to role play? Are you managing metagaming? Now, this doesn't mean that every session is the same. You don't need to pander to every player all at once every session.
Ensure the Party is Flexible
Make sure that the characters being played actually belong together and work well. Part of this is designing encounters to fit the party. But, if your immersive guy has all role-play spells and your video-gamey dudes are playing to "win", you will have conflict. The former will be bored by combat and the latter will be bored by role-play because their characters are intrinsically bad at those aspects of the game. So after you've managed expectations, make sure your players characters are flexible enough to handle different styles of play. Being a specialist is fun and rewarding, but turning your character on and off for different encounters is not. Make sure everyone can fight, everyone can roleplay, everyone can solve puzzles or whatever. It's okay to play a character that's good at one of those things and bad at the others, but it's not okay to ONLY play when your character is best at it. So make sure everyone is engaged in every activity.
Be Flexible Yourself
After you've set expectations and had a few sessions, don't be afraid to have a session that steers a little towards one type of play. Try to engage your video gamey players in some roleplay or get your role-players in some combat. My gut tells me the non-video-gamey players are perhaps more experienced and/or more flexible. At the very least, they seem to more open to a wider variety of game styles, whereas, in my experience, video-gamey players tend towards a singular style of play. So forgive me if this is directed a little at them. Engaging your players in new styles of play is a question all it's own. But, to speak very little of this problem, reward them for engaging in the different styles. More importantly, find the things that really engage them! Let each player have their time in the spotlight and make sure when they are that other players have fun as well. Better said than done. Your players need to be self-conscious of this too. They need to let fun happen for the other players, even if its not as fun for them.
Most importantly, roll with the punches. Some of the best sessions come from unexpected moves from the players. A recent example for our group was spending time in town creating costumes for our pirate crew. We had a lot of fun and none of us knew we wanted it coming in. So if something interesting starts to occur, let it happen! Don't plan too hard.
Manage Agency Accordingly
Make sure when a player is trying to speak with an enemy or any NPC that your video-gamey players aren't jumping in headlong. Even if they say "I attack", you have the power. Accept that input and let them know what happens, even if the result is "Give this player another moment". And vise versa, if a player tries to open up role-play mid battle, they don't get to speak for 5 minutes in a single round. Control your players if things get out of hand or if one type of player tries to steal the spotlight too often or too long. But make sure you're receptive to the wants of your players. Keep managing those expectations. If you control agency, make sure they know why. "Player A, i see you want to battle, but let Player B speak a little bit longer, or else join in the role-play naturally if you can". "Player B, I see you want to open dialogue mid-battle, but as long as everyone is fighting, it doesn't make sense for these Goblins to listen to what you have to say"
Get together, set a style, branch out from that style sometimes, reward flexibility, make sure your players are letting fun happen to other players.