No, you’re not imagining things. I do believe there’s actually some strategy to the game of Skip-Bo. And just to set the record straight, luck of the draw is a material part of the game. That being said, a bit of smart play can tip the scales in your favor.
The first thing to remember is that the goal is to empty your personal draw pile before your opponent(s) can empty theirs. Everything else should revolve around that goal. There are two elements of Skip-Bo that you control: playing a card to one of the center piles and playing a card to one of your discard piles. Both of them involve strategy.
The Center Piles
You’ll have as many as 4 options in the center to place your cards. But really, you only want to care about a) the one that is closest to the number on the top of your personal draw pile and b) the one that is closest to the number on the top of your opponent’s draw pile. You shouldn’t be throwing down cards simply because you can. The most important cards in your possession are the ones leading up to the number on the top of your draw pile. Hold onto those until you have what it takes to play up to your number. Don’t play them early and simply hope the center piles magically work their way right up to your number. If you play them early, you're just setting yourself up to be blocked, and then you're back to relying on the luck of the draw.
Likewise, you want to use your cards to block your opponent. If they need to place a 7, and you have a 7, place yours before they can, and now that pile is worthless to them. It’ll take them that much longer to get their 7 played because their next best option requires more cards to get back up to a 7. This is more crucial in a 2-player game, where a blocked card is about as good as playing your own. In a 3 or 4-player game, you can assist with a block and force other players to use up cards they may not have wanted to play. Let’s say the player to your right needs to place a 7 again. You don’t have a 7, but the player to your left has one in their discard piles. You can build up to the 6 and then leave them responsible for finishing the block with their own 7. (And don’t forget to point this out when it’s their turn.) Not only did the two of you just work together to block a common opponent, but you forced the other player to use up a 7 that they could have used later for their own benefit. You essentially forced their hand.
The Discard Piles
Your other opportunity to control your own destiny lies in the discard piles. They’re not a junk yard of unwanted cards. Rather, they act as an extension of your hand of cards that will be used in the future to assist you. You have 4 discard piles to work with, and it’s important to keep these piles organized in one of two ways so that you can get to the cards when you need them. First, you can dump duplicate numbers into one pile. If you put a 2 on top of another 2, you still have access to a 2 when you need it, and you’ve avoided using up another precious pile with a 2. Another strategy is to stack numbers in descending order. If you put a 9 on top of a 10, you can later play the 9 first, and then the 10 right after it. It’s best not to get too fancy by stacking many numbers in a row. You’ll need to use the top card to start the chain. If you can’t start at the beginning of your chain, the rest of the pile is dead to you.
To hide what you have and what you still need, it’s best to discard numbers that are high. If you have to play a 5, and your opponent sees you have a 3 and a 4 available in your discard piles, they’re less likely to play a 1 or 2 from their own hand. Instead, keep that 3 and 4 in hand and discard an 11 or 12. You may be able to trick your opponent into a false sense of security, and they’ll play the 1 or 2 that you still need to get up to the 5.
Skip-Bo isn’t a deep or a serious game. It’s often played to simply pass the time or with people who enjoy card games. That being said, it can’t be written off as a no-skill game. Hopefully, these few subtle bits of strategy will allow you to enjoy and respect the Skip-Bo a bit more.
If you are far enough from the card you are trying to play from your pile, it sometimes pays to go ahead and play some cards towards that number from your hand before you have all of them that are needed. The reason is that by playing cards from your hand you will be able to draw more cards on your next turn. This especially makes sense if you are able to empty your hand because it gives you a completely new hand of cards. (This is similar to "card advantage" in games like Magic the Gathering.)
Similarly, if you have a play you can make that doesn't help you or your opponent, in many cases you should play it since you will draw a replacement card that may be useful to you on the next turn.
I think Skip Bo is probably 90% luck, but you're absolutely correct that careful management of your discard piles and proper play will win you the game that other 10% of the time.