For readability, I restructured the query... starting with the apparent top-most level being Table1, which then ties to Table3, and then table3 ties to table2. Much easier to follow if you follow the chain of relationships.
Now, to answer your question. You are getting a large count as the result of a Cartesian product. For each record in Table1 that matches in Table3 you will have X * Y. Then, for each match between table3 and Table2 will have the same impact... Y * Z... So your result for just one possible ID in table 1 can have X * Y * Z records.
This is based on not knowing how the normalization or content is for your tables... if the key is a PRIMARY key or not..
Ex:
Table 1
DiffKey Other Val
1 X
1 Y
1 Z
Table 3
DiffKey Key Key2 Tbl3 Other
1 2 6 V
1 2 6 X
1 2 6 Y
1 2 6 Z
Table 2
Key Key2 Other Val
2 6 a
2 6 b
2 6 c
2 6 d
2 6 e
So, Table 1 joining to Table 3 will result (in this scenario) with 12 records (each in 1 joined with each in 3). Then, all that again times each matched record in table 2 (5 records)... total of 60 ( 3 tbl1 * 4 tbl3 * 5 tbl2 )count would be returned.
So, now, take that and expand based on your 1000's of records and you see how a messed-up structure could choke a cow (so-to-speak) and kill performance.
SELECT
COUNT(*)
FROM
Table1
INNER JOIN Table3
ON Table1.DifferentKey = Table3.DifferentKey
INNER JOIN Table2
ON Table3.Key =Table2.Key
AND Table3.Key2 = Table2.Key2