It sounds like you are questioning if you need to split the master table up because there are so many columns. The short answer is no. I'll touch on a longer answer below.
In a simple way of looking at databases, it's about groups of datum and what those groups represent. Relational databases being relationship, or links, between groups of datum. So, when you think about what goes in a table, or group of tables, you are working out aspects of some "entity" by way of the data that represents this thing. As you already know, this is done with a master table and one or more child tables.
As an example, an employee. We have a name, dob, id number(s), address, phone number, hire date, and so on. Some of these things are 1 to 1 some are 1 to n. That's how we generally break out where things go from a design point of view. That gives us a master table and some number of child tables.
Most modern databases will not have a problem with a master table having what you think of as a large number of columns. Ten, twenty, a hundred, none if that matters to the database. So, from a logical design point of view there is no reason to break-up that master table. However, the real world and theory do not get along all the time. I must stress that these times are RARE, often a different way of looking at the data will allow you to express it in a different way and avoid the issue. If you find yourself having really huge numbers of columns, ask why they are there and try to look at them from another point of view.
Back to the employee example, phone number. There could be several numbers here. So do I make a column for home phone another for cell phone and yet another for work extension? I may, or I may make a child table for it. That table would have three fields, id, category, number. So, what looked like three columns in the master table is in fact moved to a child table. Same data, different way of looking at it.
I think this maybe close to home for your case, but I admit that I am guessing here. I could see a set of stats that represent a character looking like they are part of the master table but really, they could easily be express as a child table. You mentioned basic attributes and skills, both of which would raise a red flag for me if they are part of the master table. Again, I am making some assumptions based on my rpg experiences with both computer and pen&paper games. As your game evolves you may well find a reason to add a new skill, you may even add a new base attribute. You may change or throw out an existing skill or base attribute. Do you want your database to change too? Ideally, no your don't want to have to go back and change your database structure and then the code for the database layer and then system logic code layer and then the UI code layer. You want to changes like that to affect as little code as possible. So, maybe you have a skill table, in which each row is a skill. Likewise, a base attribute table with each attribute as a row. Note that I say row not column in these cases, just like with employee phone number.
I feel myself beginning to ramble, so now I stop.
So, that's a longer answer. To summarize it, no you don't need to break up a master table because it has many columns HOWEVER you do want to analyze those columns to make sure they can't be expressed another way, like child table rows.
Hope that helps.