In situations where the game has more than 2 threads of significance, hyperthreading on an i3 can/could help via the following:
A: Less CPU cycles are wasted deciding what to do with CPU cycles. The software level simply assigns threads out across logical cores, and the hyper-threading acts, for lack of a better way to describe it, like a dedicated scheduler, maximising instruction throughput by engaging instructions on as many available cycles as possible. (makes use of available idle cycles that would otherwise have gone unused while waiting for a fetch from cache or memory to continue the instruction)
B: Hyper-threading can allow executions to occur both across the integer (X86) and FPU resources of the CPU simultaneously. If the game has a highly FPU dependant thread that might normally spill over onto a 3rd core, it's possible for hyperthreading to run that extra thread seamlessly, without any noteworthy slowdown to other running threads, right alongside other instruction loads on the same physical core.
Gaming performance generally shows little to no improvement from HT when comparing CPUs that already have 4 physical cores, since there aren't many (probably none) examples of games that spread out a significantly diverse enough instruction load over more than 4 cores. HT just doesn't even have an opportunity to help. In the few games that do have the ability to scale out to larger numbers of cores, hyper-threading provides no benefit because the instructions being called by all of the generated threads are requesting the same CPU resources as they would be if run as fewer threads.
The benifits in gaming for the i3, over say, it's dehypered pentium cousins, varies, however, when it does really kick in, it can make some noteworthy improvements. On the overall, based on the comparisons I've studied, HT accounts for about a 5% average improvement in gaming performance on a dual core, clock for clock, over that of a non-HT pentium. In the few titles where it does seem to make a useful difference, it will improve those all important minimum frame rates by as much as ~30%.