You could also get from Roku the $20 Streaming Stick Voice Remote
(RC127 or RC150), or the $30 Enhanced Voice Remote
(RC135 or RC193) if you want headphone jack.
See below, I had a Roku 3 (4200X) paired to both RC127 and RC135 remotes awhile back. With both remotes, I could "Set up remote for TV control" in the menu. Voice commands and controlling TV power/volume worked with both remotes. The headphone jack (and I think A/B buttons) worked with the RC135, no remote finder though.
You could also open the secret menu to mess with IR codes or HDMI-CEC commands. Sample screen:
As to why Roku only advertises the older Gaming Remote
as compatible with the Roku 3, my guess is the gaming motion control which is only present in that particular remote. Without it you wouldn't be able to continue playing some legacy Roku 3 games that require
motion control, but this is probably of shrinking importance to most people (who might prefer to trade it for TV power and volume control via IR). The highest profile motion games were the licensed Angry Birds titles that were bundled with old Roku SKU's, which are no longer in the Channel Store (so only applicable to existing installs). Games that are also available on newer Roku models don't rely on motion control.