I have Cakewalk Sonar X1/Expanded. And a Fantom G8 and a cheap MIDI controller.

I wanted to use the soft synths at home with the cheap MIDI controller but found my desktop's sound card latency to be too large to just play for fun.

So I bought a Roland UA-25. Great! I can play along just fine now.

But here's what I don't get. Why can I play computer games with perfectly synchronised sound effects - but I can't play my soft synths in Sonar without awful and noticeable latency? What is going on? Obviously my sound card can pump out sound extremely responsively.

So I just don't get it. Can someone explain it to me?

Playing games your soundcard drivers don't need to take the incoming MIDI-signal, your software/soft synth doesn't need to calculate it into audio and then feed it back to soundcard.
Playing recorded music has got little to do with the tasks of a DAW. I'm sure your computer could play CDs with the integrated chip without problems.

Usually you can run simple things with soft synths with the onboard chips if you find the right driver and buffer settings, but it depends very much on the soft synth used. Some are very heavy on the CPU.
The free ASIO4ALL driver has helped many who use integrated soundchips. The MME drivers, which often are the only ones the integrated chips undestand are the oldest and poorest there is.

Its in the way they are built. Factory cards are not designed to handle the huge data load we put on them. they are designed to play one wave or MP3 at a time to a movie or game.  They can handle that quite well. 

We are playing back multiple waves at a time and forcing the card to convert several midi tracks into sound and do it all in real time as well as process the various FX in the audio tracks, again in real time. A factory card simply chokes or delivers the synth sound as fast as it can but for us, that sound arrives at the speakers much to late to be useful.  

About the most delay we can deal with is in the 10ms range..... start getting longer than that and musicians can hear the delay. Most good cards that we all use easily deliver 8ms latency or less. 

Add enough synths, FX and tracks and you can get the good cards to display their weaker side too. Everything has a limit. 

What extra data load does a sound card receive from a DAW as opposed to a computer game?

I presume that Sonar is using the Intel or AMD CPU to calculate the 2-channel audio output. This audio output should be no different to a pre-recorded WAV file.

If there is going to be latency anywhere it would be in the CPU. And yet the DAW responds far better with a USB low-latency sound card than a built-in sound card.

Update: I tried the ASIO4ALL free driver and, indeed, this is far more responsive on my laptop sound card. Great!

It is entirely based on the drivers written for the soundcard. Usually cheaper sound cards aren't used for low latency recording or playback so they don't bother.