Theory:

“Here they are at last!” she cried. “Just in time for tea, and don’t they look as if they were muddy up to the eyes!”

Framton shivered slightly and turned towards the niece with a look intended to convey sympathetic comprehension. The child was staring out through the open window with a dazed horror in her eyes. In a chill shock of nameless fear Framton swung round in his seat and looked in the same direction.
Explanation:
 
In the previous paragraph, we saw how Mrs Sappleton suddenly brightened into alert attention. She then exclaims, "here they are at last!", revealing that she has some visitors. Furthermore, her exclamatory tone suggests that the visitors are people she had been eagerly waiting for.
 
She then states that they have come just in time for tea, and she adds that 'they look muddy up to the eyes'. Although she doesn't explicitly mention the identity of the visitors, it is evident from her lines that she was talking about her husband and brothers. Moreover, the line 'they look muddy up to the eyes' may suggest two things. The explicit meaning is that they look dirty as she had feared. However, the second meaning could be terrifying, or at least to Mr Nuttel. To recall Vera's story, the men died in a piece of bog. So, the line suggests that the men, as they looked muddy up to their eyes, must have come out from the very bog in which they had died.
 
As Mr Nuttel was horrified, he shivered slightly. Soon he turned to face the niece, with a look intended to convey sympathy and understanding. He had thought that Mrs Sappleton has gone completely crazy and were seeing things that weren't there. He probably never imagined that the three men could be walking towards them. To him, they were dead, and the dead never appear before living beings.
 
So, when he turned towards Vera, he was more astonished to discover a bewildering shock and terror in her eyes. She was staring out through the open window as if she couldn't believe what she was seeing on its other side. Frozen by shock and overcome by a nameless fear, Mr Nuttel turned around in his seat and looked out through the window.
 
If you had noticed, Mr Nuttel knew what he would see when he turned towards the window. Mrs Sappleton's announcement and the "dazed horror" in Vera's eyes were sufficient enough for Mr Nuttel to know that something unfathomable was happening. He could see that Mrs Sappleton was right and that the men were indeed approaching-- but from the dead, of course.
 
Meanings of difficult words:
 
S.No
Words
Meanings
1
ComprehensionThe ability to understand something
2
Dazed
Unable to think or react properly, especially due to an emotional or physical shock
3
HorrorAn extremely strong feeling of fear and shock
4
UnfathomableSomething that cannot be understood or explained, usually because it is very strange or complicated
Reference:
National Council of Educational Research and Training (2008). The Open Window – Saki (pp. 55 - 61). Published at the Publication Division by the Secretary, National Council of Educational Research and Training, Sri Aurobindo Marg, New Delhi.