As the web-resources on this is sparse, I will, for the benefit of future searches, begin by listing the address modes for IA-32 Assembly Language (NASM) and then follow up
In NASM syntax, that instruction should be MOV EBX, MY_TABLE. What MOV EBX, [MY_TABLE] would do is load the first 4 bytes located at MY_TABLE into EBX. Another alternative would be to use LEA, as in LEA EBX, [MY_TABLE].
In this case the tutorial is right. MY_TABLE is defined as an array of words. A word on the x86 is 2 bytes, so the second element of MY_TABLE is indeed located at MY_TABLE + 2.
That tutorial is not even valid NASM code. For links to x86 guides / resources / manuals that don't suck, see the x86 tag wiki here on SO.
MOV [EBX], 110 won't assemble because neither operand implies an operand-size. (I think even MASM won't assemble it, but some bad assemblers like emu8086 have a default operand size for instructions like this.) mov word [ebx], 110 would do a 16-bit store.
MOV EBX, [MY_TABLE] will assemble but it loads the first 2 words from the table. mov ebx, MY_TABLE will put the address into a register.