From the pictures I get that the relay used is a Songle SRD-05VDC-SL-C. From google I find a data sheet for that, which tells me that the coil draws a nominal 71mA https://www.ghielectronics.com/download ... elayX1.pdf
. Actual GPIO pins won't supply that much current.
However, actual GPIO pins don't need to supply that. The relay board will draw that current from a pin on the GPIO header, but that's a power pin, not a GPIO pin. The GPIO signalling pin itself only needs to provide the power to switch the optocoupler (and actually then it's sinking the current, ie, pulling current in, not pushing it out). This is why it works.
However, I wouldn't do that, because with the jumper in place I think the relay board will pull the GPIO up to near 5V when the GPIO is not sinking the current, and the GPIO won't like that (ie, you're risking damage to your Pi). What you should do is remove the jumper, connect the RY-VCC to the 5V pin on the GPIO, connect the VCC pin to a 3.3V on the GPIO header, and the input to whatever GPIO you're using. The potential headache is that the optocoupler might not work at 3.3V (depending on its specs, and I'm not going hunting for data sheets on that just now).
For you, the fastest thing to do is try it - take off the jumper, connect a 5V supply pin to the RY-VCC and a 3.3V supply pin to Vcc, and a ground, and the GPIO controlling signal, and see if it works. If it does work, that's better than leaving the jumper on and risking your pi. (Or you could just try touching a wire between the input pin and the ground pin and see if that makes the relay switch)
If it doesn't work, you could try it with the jumper in place, but you might be putting too high a voltage on the GPIO pin when the relay is not switched on. That would be bad for your Pi. In theory you can calculate what the voltage you're putting on is, but you need to know stuff you don't know. If you can lay your hands on a multimeter it is easier to disconnect the input pins, connect up the power supply and just measure what voltage appears on the input pin - if it's more than 3.3V you shouldn't really hook it up to your pi.