That product's marketing is deliberately deceptive. It's not just a 26dBi antenna, it's also (if its specs can be believed) a 2000mW (2 watt) single-stream 2.4GHz 802.11n USB Wi-Fi adaptor.
Let's deal with the 26dBi part first.
Please note that an antenna is just a chunk of metal in a shape that helps certain frequencies of electromagnetic energy radiate out in certain directions. "dBi" (deciBels relative to isotropic) is a measurement of directional gain; that is, how well the shape of the antenna focuses the energy in the desired direction, in comparison to a theoretical "isotropic" antenna, which is an antenna that radiates energy evenly in all directions in a complete sphere. "26dBi" means that your antenna's shape sends about 400x more energy in the desired direction than an isotropic antenna would.
Since an antenna's dBi measurement (its directional gain; its ability to focus energy in the desired direction) is based on its shape, you can't change its dBi with a Windows setting.
Now, about the 2000mW part. 2000mW (milliWatts) is about 33dBm (deciBels relative to 1mW). That's a measurement of power, and the power output of a Wi-Fi card is controlled by a Power Amplifier (PA), and Wi-Fi cards are generally designed so that their PAs' can be controlled with software.
HOWEVER, Microsoft has never made a standard Windows UI/API for adjusting a Wi-Fi card's transmit power. Instead, every vendor of Wi-Fi drivers for Windows that cares to let you adjust the transmit power of their card has to create an Advanced Driver Properties setting for this. So go into the Advanced Driver Properties settings for your Approx APPUSB26D USB Wi-Fi adapters's driver, and see if it lets you set a lower setting.
By the way, it seems to me that 2W of power is still not a lot. Cell phones can use up to
5W 2W (IIRC) depending on frequency band and local regulations. A traditional incandescent night light uses a 4W bulb. Even if your roommate's head was directly in line with the direction your 26dBi antenna + 2W Wi-Fi adapter was pointing, I wouldn't expect it to cause headaches. And if his head isn't in line (or nearly in line) with the antenna beam, then he should have nothing to worry about, because high-gain antennas focus all that energy in that one beam direction, so a lot less energy goes out in other directions. So as long as you're not in the beam or in some place that a lot of energy from the beam gets reflected/scattered, you're not getting as much energy as you would from, say, a typical omnidirectional (in a 2D plane) dipole stick antenna.