Did you even read the article? The article's description of "beat" doesn't conflict with the musical term but yours does. In fact the article even relates beats to tempo and describes the results in terms of tempo. This is about tempo detection.

The reason this technique is called "beat detection" is it can be used to collect the individual beats from the stream contrasted with knowing the just the tempo doesn't tell you where the beats are exactly (and doesn't help a lick with finding the off-beats.) Tempo detection is only one product of these algorithms, and guesses can be constructed from any of them, though sometimes additional heuristics are needed.

The accuracy of the LPF technique is well worth criticizing. Yes, it's fairly good, but it's not the best one we have and the article says part 2 will describe a better technique. I should note that even organs and vocals can create transients that are often associated with beats. The LPF probably does better simply by eliminating false-positives.