First, a caveat: "standard" pronunciation doesn't really exist. Aside from the general absence of official standardizing bodies in English, there is too much variability in the area of pronunciation for there to be even an unofficial standard for pronunciation as a whole (as there is, more or less, for English spelling).
The following part of this post is just about the pronunciation of this word at the present time.
I wouldn't consider ['a:rtʃitektʃə] a usual American English pronunciation. For one thing, American English is typically rhotic, so I'd expect word to end in /ər/ (that is, [ɚ] or [ɹ̩]) rather than [ə].
And to address the main point of your question, I've never heard it pronounced with [tʃ] instead of [k], and this sounds like a mispronunciation to me. ("Sound like a mispronunciation" is a description of my mental reaction, not of any objective fact about the speaker's pronunciation.)
The general "rule" for pronouncing "ch" in words from Greek is to use /k/, as you may already know. There are some words that violate this rule for all speakers: e.g., the word cherub(im) is pronounced with /tʃ/ even though it comes from a Greek transcription of Hebrew
כְּרוּב (which starts with /k/ in Hebrew). There are other words that violate this rule only for some speakers, such as lichen. Whenever you have the option of following the rule, as with lichen and architecture, I would recommend using the pronunciation with /k/.
The etymological reasons for the use of /k/ in archi- but /tʃ/ in words like archduke are fairly complicated, and I don't think they're relevant to your question. If you're interested in them anyway, you can look at the answers to Etymology and pronunciation of arch-, archi- and What determines the pronunciation of the prefix 'arch-'?.
The following part of this post is about the pronunciation of this word in the mentioned time period: 1928-9.
As far as I can tell, the situation hasn't changed that much between then and now. I know of an American "Pronouncing Handbook" from around 1873, by Richard Soule, that says to pronounce architect and architecture with /k/ rather than /tʃ/: this suggests that a non-zero amount of people pronounced architecture with /tʃ/ in Soule's time, but it also indicates that prescriptive prejudice against the /tʃ/ pronunciation was already established in 1873, and I don't think that prescriptivist attitudes about this topic would have changed much by the 1920s.
After listening to the linked video, something else that stood out to me about the speaker's pronunciation is the stress: I would transcribe his pronunciation as /ˌɑrtʃɪ'tɛktʃər/ or /ˌɑrtʃɪ'tɛkʃər/, with primary stress on the second-to-last syllable. This is not the way I pronounce the word, but it agrees in this regard with the transcription in Soule's handbook. This may have been an area of change in the pronunciation of this word in American English over the past century or so.