I agree with @NickCox : I think the mistake is in the first line of your post, where you define "bimodality coefficient". I Googled and found Pfister et al (which references SAS/STAT from 1990). That paper indicates problems with BC that are quite similar to the ones you found and recommends Hartigan's dip test, instead of BC (or in addition to it). The dip test is available in R through the diptest package.

The SAS documentation also mentions problems with BC, in particular

Very heavy-tailed distributions have small values of regardless of the number of modes.

The long tail of your second distribution is probably lowering the value of BC.

In short, the problem is in the formula, not in your code. There is, as far as I know, no perfect measure of the number of modes.

I agree with @NickCox : I think the mistake is in the first line of your post, where you define "bimodality coefficient". I Googled and found Pfister et al (which references SAS/STAT from 1990). That paper indicates problems with BC that are quite similar to the ones you found and recommends Hartigan's dip test, instead of BC (or in addition to it). The dip test is available in R through the diptest package. In addition, the kurtosis in the formula is supposed to be excess kurtosis and you appear to not have adjusted for that (although I am not certain of this)

The SAS documentation also mentions problems with BC, in particular

Very heavy-tailed distributions have small values of regardless of the number of modes.

The long tail of your second distribution is probably lowering the value of BC.

In short, the problem is in the formula, not in your code. There is, as far as I know, no perfect measure of the number of modes.