Yes, it's definitions possible that the black with white stripe is the same as blue. Though you might find that the black is blue, and the black with white stripe is black.
In either case it won't matter, if you get it wrong you'll just have to switch them.
Your receiver and remote is designed to solve a problem: someone trying to put a fan and light where there are only two wires between fan and light switch. (And often the box is not rated for a fan either.)
You don't have that problem.
At the light switch location, you have a built-in I don't know what that is. Is it a lamp-only dimmer with an on/off switch for the lamp? Is it a dimmer for the lamp and switch for the fan? A switch for the lamp and speed control for the fan? I cannot tell. What to do depends on what it is. It's possible you don't need this module at all.
If you use it, you cannot stack two fan controls or dimmers. So you must decide which to use. The two wires of input to the control module must be undimmed. So take apart that thing on the wall and figure out what it does. If any wires bypass the thing, you can use that. If a wire is controlled by the switch and not the dimmer, you can use that. Otherwise that thing will have to go. Replace it with a switch or blanking plate.
Possibly a shame, the thing may be a better fan controller than what you just bought. Not wireless of course, but wireless ones can be hokey. If it's more than just a dimmer, you might keep it in a box for if you can use it later.
If you replace with a plain switch, switch the black wire up to the fan and cap off the red wire on both ends. If you replace with a blank plate, wire nut the black from supply to this black and again cap the red.
Best Answer
It would be helpful to know what devices were powered by the black / yellow / red wires. Providing more information will make it easier for others to help you. It would also be helpful to know if you are working in a 120V environment (USA) or 240V environment.
I would attempt to identify the hot and neutral wires with a volt meter. This is the minimum. If you do not have experience working with volt meters, I suggest that you find someone that does to help and provide safety guidance.
It would not surprise me if the red and black potential difference was 120V (assuming you are in the USA).
Drawing a diagram is helpful to understanding the wiring system.