A couple of things first. I think this post would generate more feedback and faster responses in the Formulas section of the forum. Lastly, you may benefit from rethinking your base layout, where you split the data across 2 or more tables (Skills in one table, people in another). This will allow you a lot more flexibility in the long run and be much easier to manage.
Now, to your original question. Airtable doesn’t currently support a “COUNTIF” formula. You really have 3 options, and it seems you’ve found one that works, to a degree. I would suggest using a formula field and combining an IF statement (to return a flag like 1 or 0) and either a SUM or COUNT from there. You may even use a ROLLUP field if you split between 2 tables.