While Matthew 26:38 may or may not be an imperative for all future generations, the thrust of it is consistent with many, many other stories that clearly do suggest all of Jesus followers should "watch and pray with me, that you do not enter temptation."
Jesus tells these parables to his followers, all of which could be said to varying degrees are an admonition that one watch for the return of the Lord, so that you are not caught unawares. And, as Peter reminds us of the implication, "Seeing that all things will be ended in this fashion, what manner of life ought we to live? We ought to live holy lives."
Parables which teach this "watching and waiting, being prepared" aspect:
Parable of the Foolish Virgins Matt 25
The foolish virgins who are not prepared are not allowed to enter into the feast.
Parable of the Wedding Feast Matt 22, Luke 14
The wedding guests who did not eagerly anticipate the joy set before them were not invited, those who arrived unprepared were cast out into the darkness where there is "weeping and gnashing of teeth".
Parable of the Laborers in the Vineyard, Matt 20
The reward for those worked, regardless, but who stayed until the end, was the same.
Parable of the Wicked Laborers, Mark 12
How terrible it will be for those who rejected the seemingly absentee vineyard owner...
Parable of the Talents, Matt 25
Those who labored until the return of the Master were rewarded.
Parable of the Wheat and the Tares, Matt 13
At the end, everyone's deeds will be exposed.
'The harvest is plentiful, but the laborers are few', Matt 9.37
Again, rewarding those who labor
'If the man had known when the thief would come.' Matt 24:43
A general admonition towards being prepared.
And note - this was just from memory, and pretty much all of these were from the same book of Matthew. As such, even if this specific verse may just be for those disciples with Jesus, the general principle seems to be pretty much everywhere else around it - so its inclusion probably can be taken more generally.
This teaching is also not even unique to the Gospels. Paul picks up on it, and even Genesis (think Cain - Watch and be on your guard, for Satan is seeking those whom he can devour) and Chronicles (For the eyes of the Lord run to and fro, seeking those upon whose behalf He can show himself strong.)
Thus, regardless of the proof texts used to support the claim, I think it is safe to say that the whole Biblical witness would support it, even if this verse itself were clearly categorized one way or another.