My suggestion is to add a column with checkboxes in the emote list panel. These represent a selection group for a random autoplay functionality of the selected emotes (with hover tooltips to help understand the intention of the checkboxes function). I would suggest it to be interactive so selection could be done on the fly even if the "Randomizer" is active.
I supplied some retouched UI design ideas
1) "Randomizer" toggle icon besides the store icon, to make the most slim design. The "light blue" color of the UI color scheme would indicate that the "Randomizer" is active. Hover tooltip to help understand the intention of the icons function.
2) More visible "Randomizer" button, that either toggles between the "Randomize on"/"Randomize off" text or "Randomize" with the "light blue" color of the UI color scheme to indicate it is active. Hover tooltip to help understand the intention of the buttons function.
3) Same as (2), but with a duration setting for how long a single emote loops (eg duration range: 5 - 30 sec) before the next random emote in the "Randomizer" group is played.
My favorite version is (2), and with the duration setting from (3) in its own "Emote" section in settings panel. Users won't probably change that setting to much once initially setup. So, in that way it won't clutter up the emote panel design further than beyond (2).