The piece shown in the question is from the Punjabi psalter of 1908, which compiled the 150 psalms into a collection metrically appropriate for the Punjabi language. The complete collection can be found at http://tehillimresources.com/. The particular psalm (Zabur) in question is found with Zabur 39, at the bottom of PDF page 3.)
Notice that in every bar with "too many beats", one of the notes has a downward stem and is of the same duration as the preceding note. This is an indication that it and the preceding note should each be sung at half their value. When this is done, the notes exactly match the expected meter.
This "dual" notation is to accommodate verses in which the corresponding words have different numbers of syllables.
Here are the opening few measures, re-notated according to more familiar conventions.