dc42:
If it's a 4x4 keypad, then you don't need all 8 ways of the 4051, you only need 4 ways. So you only need to drive 2 of the select lines of each 4051. Plus one of the inhibit pins (or both connected together) so that you also have the state of no key pressed. So you only need 5 Arduino pins in total.
He did spec a 4 by 8 matrix - not the earlier system described in the video above.
dc42:
The 74HC4051 (as distinct from the earlier CD4051) has an on-resistance of only 80 ohms typical @ 4.5V. Keypads also have some resistance because of the carbon contacts they typically use. So I don't think the resistance will be a problem.
Ah! I looked at the wrong datasheet. The resistance did seem a bit high compared with what I recalled building my Doppler scan system some (nearly? or more than?) thirty years ago.