That’s a 16MHz 18pF 50 Ohm SMD crystal. I don’t know how picky that particular design is for things like ESR and capacitive loading. If you’re using a microchip with a built-in RC oscillator you might be able to skip the crystal entirely. I recommend doing so for simple projects like this anyway, fewer parts, fewer things to go wrong. I don’t know if the 328p has one to use or not, but I assume not as those are pretty simple uCs. In any case, they’re loading it with 22pF per leg in parallel with whatever the chip loading is and coming up with 18pF, which, since you won’t get less than 22pF out of parallel capacitance, indicates that either I am clueless about how oscillator loading is actually calculated or that it doesn’t matter very much and you can probably choose a variety of values from a bit less to probably quite a bit more than 18pF and be fine (I would buy a stack of loading capacitors to tune it ranging from 7pF up to about 30 in 3-5pF steps if you really care - most designs are fine-tuned this way after initial production anyway - the board and chip loading cannot be perfectly calculated up front).
So start looking for a 16MHz crystal in the 50ohm-ish ESR range (probably 25 to 100 is fine, but you might read the 328p tech manual or other tech notes to be sure) that’s got a loading capacitance of between 12 and 30 pF and see if any of those are available. If so, get ye the thing and just do what I recommend above and swap out the loading caps (symmetrically) up or down a wee bit if it’s not making you perfectly happy out of the gate.
Edit: Ok, I did a little research because I was curious and it turns out (from this StackExchange article) that the proper equation is Cload = ((C1 * C2) / C1 + C2), in other words, the series capacitance of the two capacitors PLUS the stray capacitance seen by that lead and the input capacitance of the MCU. This implies that they are estimating the input + stray capacitance at around 14pF, so you can adjust the caps to suit another crystal’s loading needs based on that. Now, you’re changing the board and thus the stray capacitance, so I’d still urge you to buy those extra capacitors in case you can’t get the oscillator to start properly with your guesstimate.