Is there a major translation error in MN 10?
Furthermore, when a mendicant is walking they know: ‘I am walking.’
  
  Puna caparaṃ, bhikkhave, bhikkhu 
  gacchanto vā ‘gacchāmī’ti pajānāti


From my very little understanding of Pali, "gacchāmi" means "I am walking" because the verb conjugation -mi is only used for first person singular in present tense, hence the "I am" is optional. The subject is optional.

Similarly, "gacchasi" means "you are walking" but "you are" is optional because the verb conjugation -si is for second person singular in present tense. The subject is optional.

Similarly, "gacchāma" means "we are walking" because the conjugation -ma is for first person plural in present tense. The subject is optional.

However, for "gacchati" which means "he/she/it is walking", and "gacchanti" which means "they are walking", a subject is not optional and must be clearly specified because it is not obvious from the verb conjugation who it is referring to.

Of course, in continuing conversation, third person subject (singular or plural) may be omitted, if it was explicitly stated in the previous part of the conversation i.e. implied. At least, I guess so.

Please see here.