You'd still be getting better SNR with a preamp of some sort though, right? Computer sound cards, at least in the days of old, would have a specified mic input, even for the cheapo electrets that they sold as computer microphones. Of course, if you have a microphone input on the computer, then you'd probably have a bit of built in amplification on the computer side.
The datasheet says 17.8mV at 94dB, which while it may work at line level, will be quite quiet and require a fair amount of gain to get to where you want, so if it were me, I'd probably toss in an opamp with 10 or 20 gain. The mic isn't actually stereo, it's sending a balanced signal, so you could either use a differential drive output, only drive one line, or just drive both with a single ended output... the distance between your device and the computer probably isn't long, so there probably isn't a huge benefit for staying differential. The THAT1240 series is a good choice, especially if you want an easy to get a little gain, just drop in the 1246 for +6dB, the only complaint is that it needs a wider dual supply, so you'd need four batteries, two larger voltage ones, or some switching regulators to get a split supply from your battery or two. Viable, but annoying considering how simple the current design is. There are a number of options for single supply audio class opamps that would work and some will work down to 3V levels.
That all said, what you have now will technically work. Being an electret, you could probably even use larger resistors for your biasing, the current consumption is not high, but you also probably don't need to. As mentioned, larger caps will give you better low frequency response, and if you know the input impedance on your line input, you can work out the math. Since the bias voltage is so low, though, you could just stick in a big old cap of whatever you want. 10uF is probably more than enough because the line input will probably have a decent impedance and because the mic in question is only actually spec'd down to 100Hz. You can probably get a huge capacitor (100uF, 220uF) inexpensively in a small size if you wanted to maximize the low range response with a wide variety of input impedances because the required voltage is so low.
Film caps are great, but are by no means required. A ceramic will probably do the job fine, but a lot of designs go with electrolytics and then the risk of microphonic noise from the cap is reduced to basically nothing.