Hey man,
That actually varies from person to person. A lot of it comes from individual relationships with the people and having something that can add to the team's skill sets - and being able to trust other team members in their expertise on certain matters. On our team, we are all very versed on different genres and production styles, but there still are certain aspects that certain individuals will always know best, and so we always keep an open dialogue and exchange each other every single day about what we're working on. So team spirit is the number one, directly followed of course by musical talent and passion that makes you possess an individual musical skill-set and creativity which can add to our overall palette. One of the most amazing factors of our game is its diversity. As a team, we need to ensure that we can cover that and create a lot of awesome in a lot of different ways. So only being able to write orchestral music, or only writing electronic music would undersell the awesome diversity in our game's world. And in order to do a good job in that regard, we need a really strong music team, with many different skill sets.
One point of advice I can give is: Know your strengths and limitations. People walk up to us all the time and tell us that they can write in "any genre" and "any style" - Which is incorrect. Nobody can do that. Sure, if we're talking about shallow, main-stream oriented music, yes, everyone can somehow load up NI Massive and NI Damage and get some electronic music going. And sure, everyone can pop open their Symphobia or EastWest Symphonic Orchestra and get some orchestral music going.
But that's not how you write something unique and musically cohesive that has it's own little style world that is developed and artistically invested in, and most importantly, authentic to the ear. A die-hard orchestral music listener, or a die-hard electronic music fan, will always notice if you fake or half-ass something.
So be aware of your strengths, but more importantly, your weaknesses/limitations. If I ask someone on my team "Hey can you compose something in style X?", and they say "I can do aspects X and Y, but not Z on that, I'm not good enough on that style yet." - This is totally fine. A talented person can learn anything, and most importantly, it makes me trust his decision-making and creative assessment, I can trust that they have a good understanding of what can enable us to get from good to GREAT.
If someone on my team would tell me "Yeah I can totally compose in style X", and it's not authentic to the style and uncreative in the respective genre, and he can't even tell - THAT's a problem, because then his decision making and musical understanding is flawed, and I can't trust him as much when it comes down to spearheading a musical project.
So it's definitely a misconception to think that if you apply for a composing job, you need to be able to know or do everything. Talent can learn anything. Awareness and a critical understanding of your own abilities and the high quality bar that you're trying to aim for is much more important.
Hopes this helps a bit!