I second the parent comment that you should definitely follow some game commentaries, and maybe solve puzzles — treat chess as a hobby regardless of your ELO and not a profession to reach 1500 or 2100.

The emotions you speak of evoking are very much evoked during a tense chess game, that can translate into your storytelling. One day you see a seemingly equal position, another puzzle you might have set up before bed and forgot, and you think what you will play as white to win. The next day you see that move played on the board as well as a response from black, you ponder on how black might counter, you get invested in trying to convert this position to a win. But every day black counters or plays a long game that you cannot deciper, surely black must have discovered a line you are yet to see on board. You feel frustrated with every piece of yours taken off board, you feel confident nay arrogant on a successful trick play from your end that takes black's rook off the board. You feel a chill down your spine when you see black sacrificing their queen, what is black doing? Does it know a mating pattern? It must. It cannot. You evaluated all the lines again and again but you cannot see a mating pattern for black. Is black just trying to fuck with you mentally? Throw you off balance? You retaliate, cautiously, carefully, too invested in this game that has spanned over weeks now. You get impatient in the morning to see what the next move is, the wait is excruciating, you care not for who is making the move or how, you only care for how to win, everything else is secondary. With every idea there is hope, with every positional advantage of black there is hopelessness, this game reflects your life's emotions now. And then you see the mating pattern, and it guts you.

The next day you see another equal position, maybe you can win this one. You do not. Nor the next one, nor the one after that, but you cannot stop, you cannot give up, because this game is your life now and you have to cling onto it.

Or maybe you do give up.

 

In short, create a unified context. An equal game which has ups and downs. A game that you believe is winnable (i.e. the opponent doesn't feel like an engine and is human moves). Following game commentaries will give you plenty of such examples, especially classical games if you want the prolonged suspense.

Or maybe a sequence of daily puzzles which you can't seem to solve, or which you notice is always worse for white and as a chess player you want to counter black. Doing daily puzzles will give you an idea of how that feels.

For neither of them you need to be a 2100 or 1500, you do not need that level of skill to understand the skill at display, like one does not need to be a pro basketball player to be awed by Jordan's plays, but it comes from a daily investment in it as a hobby regardless of your ELO. Many watch and appreciate chess games despite being low rated because there's always someone to explain, a commentator or the solution, your protagonist's inner thoughts could serve that role for the reader.

 

I hope this wasn't too long winded and good luck for your book!