If running a freeform RPG, this isn't a bad idea; it's better than a bunch of numbers that get ignored or suffer from subjective interpretation.
The only trick is avoiding stuff that will be overpowered and underpowered, especially in a freeform game (unless you don't care about that). For example, I see 'Intuition'. With some persuasion on the part of the player, that kind of skill can be used for a whole whack of things that are covered by other skills. And I see 'cooking'. If the players are given five and two skills only, might want to say 'oh, you get stuff like hobbies for free' (so long as hobbies aren't 'practices martial arts' or the like - artistic stuff, for example).
Alternately, say 'five important skills and two hobbies' to cover that part, and enforce that the hobbies are things for character development and/or extremely limited use. Ie, 'this guy likes doing everyone's taxes' is a good hobby skill. 'This guy likes competing in chess tournaments' is a good hobby skill (chess does NOT translate to strategy and tactics in the real world). 'This guy likes to play hyper-realistic wargames' is probably not a good hobby skill (we're back to 'can now use for tactics and strategy'), and neither is 'this guy likes to go to the shooting range a lot' (unless one enforces 'but his skill for shooting things from that hobby breaks down in real combat due to the unfamiliar pressure and situation').
If all of this is too vague, allow people to 'purchase' Basic, Advanced, and Expert levels of a skill. This way if you have two people who have 'Hand to Hand', someone with Basic can put up a fight against someone with Advanced, but ultimately lose (barring situational stuff or 'getting lucky'), while someone with Advanced just wipes the walls with the Basic guy. Someone with Advanced Control skill is an experienced mech pilot, while someone with Expert is an Ace (then make one NPC Expert+, something players simply cannot achieve for a looooong time).
Uncontested (using a skill to simply produce a desired result) use of skills should be judged by the level of the skill in play compared to 'who would we think could complete this sort of task?'. Partial success should be possible (Medical Basic cannot save someone from their terrible injuries, but maybe could keep them alive long enough for someone with a higher level to help...Survival Basic cannot help the players feed themselves and live in the Arctic, but can allow them to build a snow-hut to manage long enough for a rescue to arrive with them only mildly weakened by starvation...Driving Advanced doesn't give the ability to drive up a ramp and make an insane jump across a chasm to drive away on the other side, but maybe is enough to GET the car to the other side, but wrecked - you're walking from here...knowledge/science skills can give partial information, maybe, if high enough).
With Contested (skill versus skill) use of skills, a difference of one level (None to Basic, Basic to Advanced, Advanced to Expert) means that any contest between them is not ensured, but ultimately the higher level skill prevails (unless other skills come into play, or REALLY good use of the environment, or a specific situational advantage, or whatever). As an example, for hand to hand the Basic fighter can draw out the fight against the Advanced one (play for time?), or maybe even win if they take advantage of something the other fighter doesn't know about. A difference of two levels means the higher level skill wins 100% of the time unless someone else sticks their nose into the contest (or other skills come into play and there's a big enough difference there). A difference of three levels (like 'Nothing against Expert') means we're into 'hand to hand fighter who beats up a mob'. Equal levels gets trickier, and comes down to 'who makes more clever choices', I suppose.
Enforce players starting at Basic level in all of their skills. At different points in the game, allow them to buy a new skill, or store that 'purchase' and pay for Advanced or Expert later (say, make 'Advanced' cost two skill raises and 'Expert' cost four).
Just some easy ideas.