I've created a calculator/demo to show what's going on:
https://www.geogebra.org/classic/wg83gxjc
You can see FOVA is the game to convert FOV from (set to 106.26 by default (csgo)) and FOVB is the other game you wish to change your resolution of.
You can input the input resolution on the top left and the calculated values are below it.
All FOV angles are to the edge of the screen i.e. CS:GO is 106.26, not 90
You can see what's going on by changing FOVB in isolation and seeing the blue lines on the monitor change to reflect the same FOV as before but with the focal length of the other game
If you want finer adjustments of FOV values, zoom in and then move the FOVA/B nodes.